Let's say you'd like to claim a player off the waiver wire. Head over to the "Players" tab and click on the "+" icon in the "Action" column. You'll probably need to drop a player so that you don't exceed your maximum roster slots available, indicated by a red bar across the top of your roster. Click the box to the left of the player's name you want to drop and then hit "Submit Roster" for it to process. The system will then say that once waivers are processed you will be awarded the claim if no one that has a more favorable position on the waiver order submits a claim for that same player.
In the event that multiple claims are all submitted for a player, for instance a RB that's second on the depth chart when the All-Pro starter went down with an injury, the claim will be awarded to the team with the most favorable waiver position, or in other words closest to "1". Once a team is awarded a claim they get moved to the last possible position on the waiver order and everyone else moves up a slot, so if you didn't win your claim at least you're a one rung further up the ladder for next time (that is, IF your league uses this system).
Note: Waivers won't reset in your league during the playoffs if they are based off of inverse order of standings. The playoff teams are already set so the standings won't change.