To get into the con, you need a badge. Then, to participate in individual games, you need event tickets. While you can buy both the badge and the tickets on-site, I'd advise against it, only because it will likely mean waiting in line, possibly for an hour or more.
You can buy both your badge and your event tickets from the GenCon web site; you can have then ship it to you (if you buy them early enough), or have them waiting there for you to pick up (a much shorter line than the line to buy badges and tickets).
The RPGA has one of the large ballrooms in the convention center, and that's where all the LFR events (as well as other RPGA events, like the Delve and the D&D Open) are held.
Now, for the bad news. GenCon started selling event tickets in mid-April; I'd be very surprised if there are any LFR event tickets available for sale at this time (RPGA events are among those that typically sell out very quickly, often within the first day of ticket sales).
Now, when you buy your badge and tickets, you can buy "generic tickets", which you can use to try to get into games if there's room. The marshalls who put together the tables for each event work hard at trying to seat as many people at each event as possible, but there's a limited number of GMs available, and "real tickets" are going to have first priority for available seats. That said, you'll sometimes see people with tickets for sale or trade for particular games, so that's another possibility.
Beyond LFR and the RPGA, there is SO much going on at GenCon (including every kind of game you can possibly imagine); I'd suggest looking at the event catalog on the GenCon page to see what's available. Last year, I played in several RPGs that I'd never played before (including Battlestar Galactica and Rippers), and really enjoyed those, as well.
GenCon RPGA events fill up very quickly, but there is almost always someone available for open play - sometimes you may just have to look in the local hotel lobbies, though.
The late-night open play tends to be pretty busy, but it's full of people that simply want to play and it all ends up pretty casual.
Be sure to buy generic tickets!! Every year when I DM, I always have people seated at my tables with generics... just because people *bought* the actual tickets is not a guarantee that they will arrive for the game!
Good luck, and see you at the show
Assuming that you'll be coming in from outside of Indianapolis, you'll need a place to stay.
There's a half-dozen large hotels that are connected to the convention center via walkway, and another half-dozen within another few blocks' walk. Compared to when GenCon was in Milwaukee, there are a ton more rooms close to the convention center.
Unfortunately, many (if not all) of those are going to be sold out by this point, too. If you think getting event tickets for GenCon is bad, hotel rooms can be worse...those go on sale a day or two after badge sales go live in January or February, and the popular hotels sell out in minutes.
If you can't get a room in downtown Indy (or find crash space with a friend), you're probably looking at having to get a room in a non-downtown hotel, and driving in and out of downtown each day.
Everything Kenobi said (as usual) is entirely accurate.
Be sure to buy generic tickets!! Every year when I DM, I always have people seated at my tables with generics... just because people *bought* the actual tickets is not a guarantee that they will arrive for the game!
Absolutely. It's entirely possible to get into RPGA games on generics...but you'll need to be flexible, and have back-up plans for what to do if you can't get into a slot.
As was stated, Gen Con is something gamers actually prepare for. It isn't about RPGA and attracts tons of gamers and games that never have/will play RPGA. That's part of what makes it cool. You walk amongst Klingons, have lunch across from Darth Vader, can catch anime between slots, see lots of furries, see chain mail bikinis both fabulous and very scary, sign out a board game for a 4 AM game, sign up for a table of Paranoia based around Star Trek, demo games in the Dealer's Room, etc.
It is an amazingly huge event. Some like that it is like being in the world as it would be designed by gamers. Some like the variety. A few just like being in a genormous RPGA hall and knowing everyone is playing D&D. You can certainly only play RPGA and not run out of slots, which is fairly impressive.
Back to the preparation. Those of us repeat Gen Con goers worked with our team to get lodging. The preparation is something like being in the military and preparing for a night raid. We were at battle stations, victory a meager hotel room. Coming in late, the best option is to scour the Gen Con forums for lodging, or even ask around on these forums or on the yahoo LFR list.
Badges... I think you can still get them. Ah, you can: "Both Badge and Event Registration will close at 11:59 pm Eastern on June 27th." You can get a badge and events here. Sign up for what is still left and generics to cover the rest.
Once on site, regularly visit the booths that let you exchange tickets. People will sell back tickets often, so when they do the computers are updated and the friendly person will give you the tickets you need. And even if that doesn't pan out, you can use the generics to sit at an event.
It is good to have a fallback plan, just in case. This can be a second level 1 PC to play in case you have to replay a mod, or it can be a non-RPGA D&D4E adventure some person is running as a one-shot, or it can be a pre-4E D&D game that seems cool, or it could be a new game (suggestions: Legend of the Five Rings for RP, Spycraft for heroic play, FantasyCraft for D&D style heroic play, Shadowrun for cybertech). And, many gamers like to leave 1-2 slots open to visit the dealer's room and demo games, buy stuff, and just learn what the industry is up to. Want to play some video games? Want to get custom dice made with "I rocks" when you roll a 20 (Chessex Booth)? Want to talk a cute person into a game of Lunch Money at the demo booth? The dealer's room is a lot of fun.
Gen Con seems daunting. It is a bit, because so many of us plan for it, but like most things in life the unprepared can have an awesomely good time with no effort at all. Just jump in with both feet - get your badge, get your ticket, look online for a hotel room, have a blast.
Plan out your days if you can..which days will you go to the hall, which days are events, etc..
No matter what you will be able to play D&D, either in the delves or one of the late night adventures. If you can, try to have a couple of different level of characters with you so that you can play in any adventure.
Oh..plan on not getting much sleep...