[Disclaimer: I am no expert on pitching, having done it at precisely one conference, with mixed results. However, there is a lot of information out there on pitching, and I thought it might be useful for others if I compiled some of the sources I found most useful and told you a bit how I approached it. I want to emphasize this post is focused on structured pitch sessions, not just casual pitching.]
You have a specific amount of time with a specific literary agent (who you hopefully chose to meet with for a reason). Your mission is to pique their interest in your work (and you as a potential client) and get them to ask you to send them pages. Think of this like a sales meeting or presentation for work: you need to be professional (this includes looking professional and perhaps even making business cards - I did), prepared (if nothing else, this will keep you from being terrified), and organized (including bringing copies of your stuff, just in case).
Remember that your pitch and its success says absolutely nothing about your writing, but it may say something about your concept and how you approach it. Even an unsuccessful pitch session is a networking opportunity and a chance to learn about literary agents and receive feedback on your work from people in the know.
Pitches should usually be 2-3 minutes in length (or even less): even with 10-minute timeslots, keep it short. This means you will be speaking about 300-350 words. Does that sound like about the length of a query letter (maybe just a tad longer)? If you have a good query already, you've got a lot of your pitch.
The idea, much like a query, is to distill the essence of your book. Talking too long, and making it all about plot, will confuse/bore/irritate the agent and not give them time to ask you questions or offer feedback.
Key to the pitch is a one-sentence summary of your book to kick it off. Nathan Bransford recommends preparing one-sentence, one-paragraph, and two-paragraph pitches. That one sentence pitch can come in handy in other contexts, as well.
Here you need to walk the line between rambling and being too business-like. Rachelle Gardiner has a great post about what to include in a pitch. I found this particular post absolutely essential to walking that line as I put mine together. Kristin Nelson has genre-by-genre advice in this series of posts.
As I mentioned a couple of posts ago, I know myself well enough to say that my presentation skills are good, but my ability to talk off-the-cuff and not forget stuff is terrible (in science you never have to talk without a Powerpoint behind you, and I tend to build those with prompts so I don't forget things). So I prepared by writing my pitch out, word-for-word, and then memorizing it (yes, some things changed if they looked good on paper but sounded silly coming out of my mouth). My pitches consisted of about a dozen sentences and I structured them as follows:
Sentence 1: It's nice to meet you - I'm Lt. Cccyxx and...[something personalized about them to show you did your homework on them].
Sentence 2: I wanted to meet with you because I thought you'd be interested in my book, a work of [genre] called [title].
Sentence 3: It's a book about...[the one-sentence summary].
Sentences 4-9: [Summary of major plotline with introduction of the protagonist and perhaps a couple of other characters if essential. For me, this came mostly straight out of the query, though I found myself boiling it down even more than the query.]
Sentence 10: [Hook back to the agent. Reference something they said or some work they represented and connect it to your work.]
Sentence 11: [Theme, hopefully in a way that follows logically from Sentence 10 - this might be optional for some people but I wanted to include it to make the case that: a) I understood my own work, and b) the book works on more than one level. I also wanted to make it absolutely clear - since I am a scientist pitching a novel involving science - that I was not Dr. Dorky McDorkalot adapting my old lecture notes by sticking them in dialogue form.]
Sentence 12: My book bears similarities to [one or two books it bears similarities to - if it's a thematic rather than stylistic similarity, you probably cannot skip Sentence 11].
Sentence 13: I hope this has given you a sense of my book and piqued your interest.
Now of course if you go the memorization route, you don't want to sound like a robot when you deliver the pitch. I practiced with my wife a couple of times to get my tone down and ensure that I sounded excited (after all, this is my work and I am excited about it) but conversational, not like a third-grader delivering lines in a school play. Preparation aside, Agent 1 asked if I had memorized my pitch (and I readily admitted I had - obviously this did not count against me).
There you have it: my advice on pitching. Take it for what it's worth...and definitely click on the links, since most of them are written by people who have a lot more experience than me!