To follow a person on Quora: Go to their profile page and click the blue Follow button underneath their name. If you are already following the person, you will see a gray Unfollow button instead.
On a computer, you can also follow someone in most places where you see their name on the website (e.g. the name of an answer author): hover over the name and click the blue Follow button.
When you follow a person on Quora, your Feed will start to include their activity — answers they've written or upvoted, and questions they've asked or followed. (Note that you aren't guaranteed to see all of their activity in your feed — this depends on the amount of activity from other topics and people you're following.)