Hum the tune in your head, starting with the first note. Drag out the first note while trying to match it to a note on your instrument. Once you find your beginning note, use the key that it's in as a guide to pecking out the rest of the tune.
Write down your tune, either by writing it down in blank sheet music, or simply by jotting down the notes in the order that you play them.
Come up with a chord progression, based on your notes. Ideally, the first chord will be the key that your song is in. This may take some experimentation and fooling around, but having a chord progression, along with a lead can add a lot to your song.
Add bass notes by putting in lower notes based on your chord progression. For instance, if your progression is G, C, A minor, D, add the bass notes of G, C, A and D, in sync with the progression.
Add a beat. This may not be appropriate for all songs, but if you feel like a backbeat could accentuate the tune, try to adding something, even if it's simple. If you don't know how to add a beat, take your tune to someone who knows how to drum.
Play your tune for other people to see what they think of it. Get suggestions on ways you can improve it. When you feel that it's finished, try recording it at home or taking it into a studio.