All free agents are locked until the day of waivers...it is usually wednesday in most leagues, thursday in a few others. This is done to prevent someone from signing all potential free agents on sunday as he watches the injuries unfold during the game.
Waivers are locked, and then released based on reverse team rankings in your league. For example, the 12th rank team will have his first waiver claim processed first. The #1 ranked team in your league will have his first waiver claim processed last.
Since your team is allowed three claims, that means that currently only two teams are ranked lower than you in your league. Thus, even if the two lower ranked teams have the same waiver claims you do, you are guaranteed to get one of those three claims. Make sure you prioritize your claims.
Your friend may be able to make more claims than you at this current time, but when waivers are processed each team will only have ONE player claimed for them--the highest claim remaining on their list. He only gets to add more claims now because his team will be one of the last processed during waivers (based on rank). Therefore, he has the opportunity to add more claims because it is likely many teams ahead of him may want the same players.
see waivers under the home help page for more information.