First, this is more geared toward posting on communities, since you can do whatever you want on your own livejournal. However, some of what I say about communities may apply to your livejournal, so keep that in mind.
Second, I am making the huge assumption that you are posting your fiction to a community in order to get people, who would not see it on your lj, to read it.
Third, this is not a guide on how to write fanfiction, although there are many resources for that. This assumes you already have fanfiction written, and in a fit state to be seen by people.
So, broken down into steps, your posting process.
1. Pick the community.You want to post your fic to a community where community members will be interested in it. You probably already belong to a community that posts fic like yours, but if you don't, you can find communities by looking for common interests.
Once you find your community, read the community info. This can be found by clicking on the graphic next to its name, or by clicking on userinfo within the comm. Read this carefully. Some communities accept everything, others are only for certain pairings, genres, or mediums. If you're not sure if your fiction is what the community wants, ask the moderator. The moderator will be mentioned in the community info, and often will make their email address available. If not, it's appropriate to drop a note in their journal asking if your fic is right for the community.
If you are not a member, you will need to join the community to post. If you think you are a member but cannot post, there are two possibilities, either posting is screened and you do not have the moderator's permission to post, or, more likely, you have the community friended, but are not a member. The userinfo page should list friends and members, and if you are not a member, you need to click on the link at the top of the userinfo page that says "to join this community, click here."
2. Make the post.You probably already have your fiction written up and posted somewhere, but it's good manners to format it according to the community specifications. Some communities have a special template they'd like you to follow, others don't. If not, take a look around the community to see how other members have posted. You're not compelled to do this, but remember, you want people to read your fic, and offending or alienating your prospective readers isn't a good start.
Start with the post subject heading, in its own field. Although you may feel that "So... erm, I'm feeling nervous..." is the best reflection of your feelings, (See Appendix B,) it's not going to help readers find that story that they know was posted here last year and man, they loved it, but now they can't remember who wrote it. A good heading is Fic: [Fic Title], by [Author]. If you think it's important, you can include the rating.
Almost universally, fic have some kind of header which serves the dual purpose of letting your prospective readers know enough about the fic to be able to make an informed choice whether or not they want to read it, and also enticing them into reading it. If the community doesn't have a template, a fairly common one is as follows:
Fandom: This is really only necessary in multi-fandom communities. But if you're posting to, say, rarelitslash, you might want to let them know whether you're writing from Northanger Abbey or Genji Monogatari.
Author: If the name you like to be known as is different than your lj username, or if you just want people to know it's you.
Title: The title, obviously, but also, if it's one part of a multi-part work, indicate here by writing [1/16] following the title, for the first part of a sixteen part work or [3/?] for the third part of an unfinished work that you don't know the length of. Be aware that people will be more likely to click on finished works. If the work does not stand on its own (ie. ends with a cliff-hanger) you should definitely mention that it's a work in progress (WIP.)
Pairing or characters: Some people only read some pairings, and they may want to know what pairing you have in your fic. Some people only read het (heterosexual pairings,) others slash, (definitions vary, but generally, homosexual pairings,) so this is a good place to let them know what they can expect. On the other hand, if you feel that letting them know the pairing would be a spoiler, don't put it in! It's also perfectly valid to write "pairing: none." If the fic is not primarily focused on a relationship, you may label it "gen," for general.
Some people have favourite characters, and you could let them know that their needs will be met here. Mentioning the main character(s) in your fic is sufficient..
Warnings/Rating: Nobody wants to read something that will upset them, and presumably you don't want your readers to be upset, so it's a good idea to give them enough information about anything that might be controversial for them to make up their minds. You can be specific: "this fic contains the suicide of one the main characters," or general: "for mature audiences only, contains disturbing content," but it's a good idea, and just plain polite, to let people know. Remember, kids as old as six or seven use the internet unsupervised.
It used to be common to assign ratings to fic based on the same system used for movies. Thus, fic with explicit sexual material was NC17. However, as the MPAA has recently begun to enforce their copyright of these terms, this is not recommended. Alternate fan rating systems exist.
Spoiler Warnings: First, do you belong to a fandom with an open or closed canon? If it's closed, like Shakespeare, where one may confidently expect there to be no new works added to the canon, you can also expect your readers to be aware of most of the plot twists, and no warnings are necessary. On the other hand, in an open canon like Harry Potter, new canon is piling up and not all fans know about all of the new developments. Don't assume that just because an episode has been aired a week ago, or a month ago, that all fans are familiar with it. Television schedules can vary by several years from country to country.
For example, you could probably safely conclude that everyone knows Vader is Luke's father, but not that everyone is familiar with the events of Episode III.
So ask yourself, does your fic contain references to events that were surprising or revelatory? If so, it's only polite to warn fans that are spoiler averse. Usually it's enough to say, "this fic makes reference to events in episode x."
Disclaimer: Since you are writing fanfiction, your fiction is an infringing work in a legal grey area. Disclaiming ownership of the characters may give you some limited coverage from prosecution. In the case of fandoms where copyright has expired, you may wish to acknowledge your debt to the original creator. Example: these characters are the property of Mutant Enemy and Joss Whedon. I do not own them.
Author's notes: First, remember that no one has read your fic yet, so it's a good idea to keep this short. Anything that has to do with the writing process, you can put at the end, if you feel it's important. But this is a good place to mention your beta reader(s). First, it's just polite to acknowledge their effort, and second, it lets people know that you feel that fic quality is important, and got your fic beta read. (This is a big draw)
Summary: Here's where the hook goes that will make people interested enough to read your fic. Although it's often called 'summary,' some people prefer not to actually summarize their fic. I personally prefer to find an extremely short snippet, not more than a sentence or two, sometimes just a phrase, that I feel is representative of the mood of the fic, and include it here. Others feel this is vague and annoying, so you may wish to describe in general terms, without spoiling, the main action in the fic. You can't make everyone happy, so please yourself. The successful summary makes your readers curious and interested.
As well, although I've gone on at length, it's important to keep this as short as possible. If it's too long, readers may not even bother going through it. Here's a made up example:
Fandom: Deuterocanonical BibleOr alternately:
Title: The Fruit Discloses the Cultivation
Characters: Judas Maccabeus
Warnings: contains religious content, and historical characters in sexual situations
Author's notes: Thanks be to deity I never actually wrote this.
Summary: It's hard to ignore an elephant.
Title: Harry Potter and the Prisoner of Luuuurve
Pairing: Harry/Draco, baby!
Rating: XX for kinktastic sex and C for issues of consent.
Disclaimer: These characters belong to J.K. Rowling and rights-holders, one of whom I am not.
Author's notes: Thanks to devildoll for beta reading this imaginary story.
Summary: In which Harry Potter acknowledges his feelings for Draco and takes him prisoner.
Finally, you need to include the fic itself! Here you have a choice; you can either include the fic in the post you make to the community, or you can link to the fic in your on lj, so that all comments on the fic will be in one location. This may be especially desirable if you've posted to more than one community to announce your fic. (See appendix B) I prefer the latter, but it's up to you.
If you choose to include your fic in the community post, your fic should be behind a cut so as not to force it on readers. For information on lj-cuts, see the faq.
If you want to link to your post on your own journal, the html required is the one in the address bar once you've clicked on the post. It should look like: http://www.livejournal.com/users/yourusername/00000.html#cutid1 if you've cut the body of the fic, or the same url without #cutid1 if you haven't. If you have duplicated all the information outside the cut in the community post, it's polite to link to the cut (url with #cutid1) so readers don't have to read the same thing twice. Information on formatting links.
Some people like to link using a "fake cut." This makes a link to a cut outside the journal you're posting in look like a link to a cut inside the post. You can do this by surrounding the link with <b>( link )</b>
Congratulations! You are ready to post! Post the sucker!
Appendix A: Organizing your works:
Tags: Wouldn't it be awesome if people liked your fic so much that when they followed the link from the community they wanted to find more by you? You want to make this as easy as possible for them, if they are so inclined. Tags are very useful for this. Tagging all your fic with [fanfiction] or something like that, will make it easy for them to find the rest of your fic with one click. Tagging all parts of a multi-part work with the title of that work makes it easy for them to read it from beginning to end, even if they happen upon it a year after you've posted it. You can add more than one tag, so if you think people will be looking for only your Gundam Wing fic, or only your slash fic, you can tag things [fic, Gundam Wing, slash, NC17].
Memories: You can also add all your fic to your memories, making them available on one page. The disadvantage to this is that readers will be clicking through more or less blind, knowing only whatever information you put in the title, so if you use this method, try to include important warnings in the title.
Appendix B: Try to avoid:
Over-cross posting: If your fic would be of interest to two different comms that don't have overlapping readership, cool! Post it to both. But try to avoid posting to more than two or three, to avoid spamming the friends lists of people who have a dozen similar communities friended. This is not cool, and although it may gain you readers the first time, the second time you will find that you are being avoided.
Bulking up the author's notes: Posting your fic can be nerve-wracking, but avoid the temptation to insert something like, "this probably isn't any good...," in the author's notes. If you're not confident, keep asking beta readers for help! You can have as many beta readers as you can entice into reading your fic. Your insecurity just bulks up the author's notes and makes people less likely to read it. By the same token, although you may want to share the music you were listening to, the conversation you were having that led to this fic, or the reason why this pairing is so meaningful to you, it's best to do that in your own livejournal, rather than a community post.