You can use the Reddit app for iOS anonymously by tapping Snoo -- the little Reddit alien in the top left hand corner. From here here you tap the down arrow next to your user name then tap "Anonymous." You can leave comments when anonymous, but you can surf Reddit while appearing to be logged off. The Accounts page is also where you can add another account to the Reddit app or switch accounts.
The Reddit app for iOS is available for free on the Apple App Store. It includes an easy to use interface that makes surfing trending news and topics simpler. The app also makes reading and reacting to comments easier than the desktop version of the website. Users can also upload photos, post memes, contribute stories, join discussions, and more through the app.