The Waiver Wire can be found by clicking on GM's Office. The Waiver Wire shows players that are available to be claimed. Players salaries are incrementally reduced throughout the day, so you may find some bargains (these guys need to eat too)! You may claim a player if you don't already have that player on your roster (the same player from the same year can not be on your roster twice) and you have enough available cash to afford to claim the player. In order to claim a player off waivers, you must also release a player unless your team has an empty roster spot resulting from an uneven trade or previous release. The salary freed up by releasing a player combined with any available cash you had after your draft equals your buying power - the maximum you can spend to claim a player on waivers.
To claim a player, just click on the icon next to the player's name that you want to claim. A window will then popup showing you players from your roster that you can release to make room for the player you are trying to claim. A player need not be released if enough cash is available.
Anytime you claim a player, there is a 10% transaction fee. This means that you have to have enough cash, either from releasing a player or just left over to cover the new player's salary plus 10% more of that player's salary.
Players are claimed and released constantly as the same Waiver Wire is used by all leagues. So if you release Sammy Sosa, he may be picked up by someone else in another league or by someone in your league and vice versa.