After you draft a player, he will join your franchise and appear in your group of players needing assignment. You then have until the end of Spring Training in which to put him on your big league roster.
If you don't put him on your big league roster by then, the player will go through the Rule 5 Offer back process. The first step in this process is that the player gets put onto the waiver wire. If he is claimed by another owner, then he and his special Rule 5 status are transferred to the new club.
If he isn't claimed, he will be sent back to his original franchise. They then have 2 days to either accept the offer back for $25,000 or decline it. If they accept the offer back, the team that drafted him loses all rights to the player.
If the original franchise decides to decline the option, the player then loses his unique Rule 5 status and becomes a player with no additional rights. If a Rule 5 pick is acquired via trade or waiver claim, the new club has 72 hours to assign the player to his big league team or else the whole Rule 5 Offer back process starts again.