I've been going to the draft for years now, since the days of MSG Theater, Jacob Javits Center, and now Radio City Music Hall. Here's the rundown on how the tickets go...
The night before the draft (Wednesday night) try getting to Radio City at around 9-10PM. Wristbands will be distributed at around Midnight. Two years ago, I worked and didn't get to Radio City (between West 50th and West 51st Street, on 6th Avenue) until 11PM and got lucky because there wasn't a huge line. Regardless, I usually try and aim for 9/10 and just wait. Your call on what time you want to get there.
So you get your bracelet on Wednesday night and then on Thursday night, get there as early as you'd like to get better seating. With your bracelet you're guaranteed to get in regardless. Also, I've never seen people NOT get bracelets, so I guess you don't really have to get there too early on Wednesday night. Anyways, a line will form in the same spot as Wednesday night on Thursday. It's first come, first serve so whoever gets there the earliest gets the better seats. So if you want to sit on the bottom level, try getting there around 6 or so. There will be people camped out, so they'll likely get the best spots, but after that anything goes. I sat all the way up top 2 years ago and honestly, there was no difference. It's not like you're really watching anything.
They'll give you your goody-bag at the door (radio to listen to either ESPN or NFL Network coverage, trading cards, Campbell's chunky soup, NFL Draft backpack) and you'll be all set. Draft hats are available downstairs in the lobby for an arm and a leg, but I usually get one anyway. You get frisked at the door so if you're planning on sneaking a flask or something like that because of outrageous beverage prices at Radio City, do a good job hiding it! Or get one that doesn't even look like a flask. You didn't hear that from me though!
Keep your bracelet so that you can get in on Friday and Saturday!
PM me if you have any questions about the process, etc. I was planning on going but with the Hawks not having a 1st rounder I might just wait for Friday. If you can't make it Thursday but want to go Fri/Sat, you just have to wait outside on a line just like the night prior. Sucks because you miss what's going on inside, but with the Hawks not drafting til Day 2 it's not too bad this year.