Ok another silly question
You draft a guy but he doesn't make your playing roster does he still get paid and do you get to use him following season or does he become a free agent?
He gets cut. He then goes through a process called waivers over the next 48hrs, where any other team can put in a claim for him and will pick up his contract if their claim is successful (claims are prioritised in a similar way to the draft, so the team with the worst record gets priority if more than one team puts in a claim).
If he clears waivers he hits the free agent market and is free to sign for anyone. Any guaranteed money in his contract is still obliged to be paid by the team that cut him, but most contracts have large amounts of conditional payments which don't fall due. Consequently, if he signs on somewhere else, he'll be entitled to monies from both contracts.
Quite often, if a player is on a big contract and gets cut, teams will be reluctant to put in a waiver claim for him as it obliges them to honour the contract, but once he clears waivers there might be a rush to sign him in free agency, probably for something close to the league minimum salary for that position.
There's been some real-life examples of this happening today, just to clarify the point:
Arrelious Benn has just been cut and re-signed by the Eagles, no doubt on a lower salary than before. Cut on Friday, no-one put in a waiver claim for him, and re-signed today.
http://www.nfl.com/news/story/0ap2000000351358/article/philadelphia-eagles-resign-wr-arrelious-bennGreg Little got cut by Cleveland the other day, and has been claimed on waivers by the Raiders.
http://www.nfl.com/news/story/0ap2000000351809/article/oakland-raiders-claim-greg-little-off-waiver-wire