I do plays and musicals in community theater, and while nobody’s ever going to offer me a record contract, I can belt out a tune well enough. Like WordMan, I’m best on “character” songs. Songs that can be “acted,” that don’t always require spectacular vocal ability, but the ability to sell the song and often, to be funny with it.
I can also sing harmony parts pretty successfully, which is really useful in community theater, since they always need men’s voices in the chorus. I always say to guys who are interested in getting involved in community theater: audition for a musical. If you can even halfway carry a tune, you will probably get cast, because they always need male voices.
I am mostly self-taught, although I learned to read music back in elementary school (in the days when schools still taught that sort of thing), and that’s helped quite a bit. I think it also helps having a good ear for music. Not necessarily perfect pitch, but more “relative pitch,” being able to hear the relationship between two notes. If I sing a given note, can I know where, say, a major third above it is, and hit that with precision.
I don’t know how much of that is instinct and how much is practice, but this is where singing along with a piano is helpful. One thing you can practice is singing various intervals along with the piano, and hopefully develop a sense of how various intervals “feel.” I’m fairly sure that this is one of the things musicians study in school, so at least part of it can apparently be learned.
I am neither a music teacher nor a great singer, so I can’t give you any more solid advice than what’s helped me. I know that there are Doper professional musicians, and I believe at least one opera singer, who hopefully will notice this thread.