The way they select float riders the past few years has slightly changed every year. It's really dependent on who's running the show. For example, this past Mardi Gras was the most organized year I had ever seen.
The main way over the years, as mentioned, has been the Annual Pass sign up form. Which, is very possible to win, I have won once every year I have entered.
A few years back, guest services was able to print out tickets to ride a float pretty easily. Recently they've tightened up a lot on this and no longer hand out float rides. They'll tell you to wait outside the check in area in case there's any open spots. (The check in area was FFL courtyard, aside from last year when it was Kidzone over by Barney. It will more than likely be Kidzone again this upcoming Mardi Gras.) Guest services can grant float rides to make up for bad experiences in the park, so on, but it's not something you can usually ask for.
Waiting outside the check in area is a gamble and highly dependent on how many spots they already have that night and how many have shown up. I've found closing night to be the hardest night to get on, with weekends schools are out being the second hardest. Usually the ones in Mardi Gras polos are the ones that can give you wristbands for you and your group to ride. The only exception being when there's a large amount of open spots, then the float captains that are working the entrance can get you a wristband.
You do have to be 18 or with a parent or guardian to ride.
Overall, all the Mardi Gras staff are super friendly and will definitely try to get you on if they can. It's a really fun experience.