What exactly goes on at the draft. I know the players get picked but what else is a draw to it
I've been to four drafts (2010/11/15/17) and it's certainly not something I'd recommend for everybody. For most people, it's a lot easier to watch from the comfort of your own couch plus you get the commentary as Mr. Misty mentioned.
And if you only care about who your team is taking and are ambivalent about the other picks, then it's probably as exciting as attending a graduation ceremony.
That said, the great thing about the NHL Draft is that everybody is physically there. Not like the NFL Draft where teams are in their home offices and only a handful of prospects are there.
This year in Chicago, I accidentally stumbled on the private entrance for the NHL clubs which was on the opposite side of the FanFest. The FanFests tend to be forgettable and/or geared more for children.
So before the draft, I was within five feet of everybody who'd be on the draft floor. If you have the nerve, you can ask politely for pictures/autographs. Most of the folks were accommodating.
After players have been drafted, they'll probably be roaming around the arena. I got to have a quick chat with Jon Merrill, Adam Larsson, Mackenzie Blackwood, and Jesper Boqvist.
It's harder nowadays, but in 2011 my buddy and I snuck down into the players section for round 1. It's a different dynamic to be sitting there wondering why Brandon Saad is dropping and being able to look ten feet to your right and see Brandon Saad sweating out the picks.
If you're a local, I'd actually recommend watching Round 1 at home and attending Day 2 in person.
I'm always shocked by the amount of people who attend Round 1 and have zero clue who anybody of the prospects are. There are far fewer people on Day 2, so it's a bit easier to approach people for pics/autographs. Plus Day 2 usually starts at 10am local time (although it was 9am this year in Chicago). So hanging out at the draft on Day 2 doesn't stop me from having other plans Saturday night.
Also, I wouldn't recommend sitting through every pick. As much as a draft junky I like to think I am, by the time the fourth round rolls around, I'm not going to know much about the draftees. It's not a bad idea to grab some food and take a lap around the concourse to see who you might run into.