Song Help Request Chords from a melody?

So I've got this little melody laying around in my binder (sorry, don't know the name). I want to play the melody I have and record another track of a basic strum (rhythm I suppose?).

Now I have a decent grasp of chord construction and scales, so the basic question is, how do I pick chords for a given melody? Is there a typical proceedure for this? I would research the topic, but I don't have the terminology to give me something to look for.


Thanks!