Well, generally simple questions like this are in the FAQ section. The button on the top bar, called "Help" has questions answered. But here, I'll paste it for you:
Challange another Team or Player?
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Challenge on Team Ladders
Simple. From the Team Administration Console you will see buttons for each of your active ladders. Click on the Ladder Administration Button and you will see the Admin Console for that ladder. At the top of the page will be a full listing of every team you are allowed to challenge. Click the link and you will be asked to confirm the challenge. Click Confirm and you're all set.
Challenge on Player Ladders
You must first be logged into TeamWarfare. Next, go to the main TeamWarfare.com page. You should see information on any ladders you are currently on right above the news section. Click the "Admin" link on the right side of the ladder information for the ladder you wish to challenge on. From there, you'll see your current status, and, if you are currently unchallenged, a list of available players to challenge. Click a player's name, and you will be taken to a brief history page for that player. You will see a "Submit Challenge" and "Cancel Challenge" link at the bottom of the page. Click "Submit Challenge" to challenge this player.
You will be taken back to your player ladder admin console, and from there you can submit match communications and check on when/if your opponent accepts your challenge.