You can follow anyone you like on Duolingo. You can also invite friends to join. When you follow someone, they will show up on your Friends List, and you can compare your weekly/monthly/all time XP. On the web, you can view your Friends List on the homepage.
NOTE: This Friends List is different from your Leaderboard where you compete with 50 Duolingo learners in a weekly XP competition. You can learn more about Leaderboards here.
There, you can sort your friends by selecting the leaderboard of the week, month or all time. The highest scoring friends will be on top. This list is scrollable, so if you don't see the person you are looking for, try scrolling down while your mouse is on the leaderboard.
How to Find/Invite Friends?
At the bottom of the leaderboard, there are a few buttons. You can find your Facebook friends by clicking on "Find more friends on Facebook. You can also send someone an invite via email by clicking on "Send invite."
If your friend already uses Duolingo and you know their username or account email address, you can search for them within Duolingo.
How to Follow friends?
You can also follow people you like on Duolingo. Simply click on their name in the forums or search for them. When you land on their profile page, click the "Follow" button to add them to your Friend List. They do not have to accept your request. They can also follow you back if they want to. If they block you, you can no longer add, follow or contact them.
To block someone, follow the instructions here.