There are many ways to make someone your friend. You can offer assistance with a project, or provide comfort at a time of loss. Perhaps the easiest way to befriend someone, however, is just to smile and say "hi."
The prefix "be-" is from Old English, and has several meanings. In befriend, the meaning is "cause to be," so to befriend someone is to cause him or her to be your friend. Mahatma Gandhi once said, “It is easy enough to be friendly to one's friends. But to befriend the one who regards himself as your enemy is the quintessence of true religion. The other is mere business.”