Well, here's some cheap advice: sing along with your favorite CD's.
I like to sing when I drive around, alone, with the windows rolled up... I have a sense of responsibility to not expose innocent people to my experiments. Usually with some rock songs. My range doesn't always fit with the recording, but that just forced me to learn ways around it - expanding my range a bit and singing in a different register.
I'm not entirely absent-minded about my little undisciplined singing routine, I'm usually listening and trying to make the pitches accurate and resonant. That's about the extent of it, but I swear it's helped in some basic rookie way - I've gotten the odd compliment at kareoke and friends have said my singing isn't horrible

I've found trying to use the pitches on the piano as a guide feels unnatural to my voice, equal temperament is an unnatural compromise afterall and I wonder how wise it is to try and force the voice to do the same. In any case since I don't intend on being a serious singer I'm content to keep things simple for myself and just sing 'by feel'.