All unowned players who have cleared waivers are free agents and are available on a first-come, first-serve basis. You can pick up or drop by clicking on the Pick Up Player or Drop Player links located near the top of your Team Page. All claimed players will immediately be added to your bench for the following day (unless you are in an Invite League configured to allow same-day transactions). It is up to you to move them to starting positions.
You can drop players without replacing them, but you can only pick up players without dropping anyone if you have less than the maximum number of players on your roster. You will never be allowed to exceed your league's roster limit.
Before the start of the season, all undrafted players will be placed on waivers with those left unclaimed then being treated as free agents. You can find out the length of the waiver period for your league by clicking on the League Settings link on your league home page.