There are several ways to subscribe to a new subreddit.
If you know the name of the subreddit you want to subscribe to, select "Manage Subreddits" at the bottom of the subreddit list and then enter the name of the into the field at the top of the manage screen and tap "Add."
If you're not sure what you're looking for, you can search for subreddits to add. Tap the bacon icon in the upper left and select "Search" and then enter a search term in the box and select the Subreddits option. If you find a subreddit you'd like to add to your subscribed list, tap the "i" to the right of the subreddit name and then select "Subscribe."
You can also use the Explore function.