I made my first edit today and I was informed that the edit will not be visible to other users until it passes peer review. I assume there are edits made by others that are await peer review. How can I make myself useful and review the edits of others?
To peer-review suggested edits, you need 500 reputation. This is actually lower than it usually is: we lower rep requirements during private beta. Once you reach that threshold, you will begin to see an orangeish blob with the number of pending suggested edits in the bar at the top of each travel.stackexchange.com page.
Right now there are only a handful of users able to review edits, so Stack Exchange's Community Team members keep an eye on the queue as well, to make sure edits are reviewed as promptly as possible.