To become friends with another account, the two accounts must follow each other.
Find someone to follow
From the official website, open the Friends page by clicking on the Friends icon on the upper-right.
If you are trying to follow someone, click the icon on the upper right or the blue "Search People" button. (The blue button only appears when you have no friends)
Type in the User ID or display name and click the button outlined in red, "Follow". By clicking on the button again, you can cancel a follow.
By following each other, you can become friends.