Once I decide what song I want to learn--usually have half-learned it by the time I make the decision, since I like the song--I listen to it a few more times.

Hardest part is trying to decide which version.   Usually what I think of as the original.

Then I get all the words, either by transcribing or off the Net.    If off the Net, major surgery is usually required.   Our own Jim Dixon and a few others are reliable sources.   But otherwise, those who post on the Net are amazingly clueless--you can usually get much closer to what they're actually singing just by listening to a recording.

I make several copies of the words, and take them with me for a while. Pick out a key I want to sing in.   Have to pay attention especially to transitions between verses, and to verses which are somewhat similar--need to be clear on differences. Then I start singing it all around the house--and especially in that well-known source of good acoustics, the shower.   Then I sing it while walking on the street--going anywhere--putting it into the repertoire.   When I walk to the subway, I sing the whole way, usually according to the weather.   If it's good I sing country and western.   If it's raining I sing Irish. Doo-wop--anytime.   Real blustery--sea songs.    Unless of course there's something I want to learn real fast, including of course other genres of songs--then the weather doesn't matter.    It's about 4 long songs or 5 short songs to the subway.    Doo-wop--8 or 9 songs.

I take a copy of the words with me if I'm singing in public, but never look at them while singing. However, having them in my back pocket is a good talisman, I find.