There's also a "Popular" tab (the one with the star), where you can see the most liked photos on the network right now in a big grid of thumbnails. (Note: This tab is usually pretty dumb.)
The third way is the most complicated, but it's also the most interesting. The "News" tab (the one with the heart in the chat bubble) shows you all the notifications about liking and following. Within that tab, there are two more tabs. The "Following" side shows all the photos liked by people you're following.
This is the best way to discover new photos and the people who took them. If you find a photo in here that you like, you can tap the name to see the photographer's profile. If you like what they do, follow them, and now you'll see all their photos.
The other side of the "News" tab is the part that's actually called "News." That's where you'll see all the likes and comments on your own photos. It also shows when new people follow you.