If I have a recording of the song, I play it over and over and over and over, until my husband (who is tone deaf) can recognize the opening notes of the song and threatens divorce if I don't stop tormenting him. Thereafter I play it only in the car, since he's not there to complain, until my toddler begins to squirm and protest whenever he hears the song. By then I've usually memorized both tune and words, figured out what key I like it in, etc. Then I tend to sing it in the shower, where I have access to neither the recording nor the written lyric sheet, so I have to rely on my own memory and can see just how well I have learned it. If I like it in the shower, then I add it to my formal repertoire. If I don't feel it showcases my voice enough or my voice cannot do the song justice, then I relegate it to the "just for fun" collection in my head.
Back in school, a friend taught me a cool trick. To find out if you really know a piece, sing it with the radio or tv on at a volume to compete with your voice. If you can get through the whole thing undistracted, with timing and key and all correct, then you know it cold and can perform it anywhere.