As with anything else, the more one does things, over time, the better one tends to do them. Progress can be faster with a teacher or books/videos/internet, etc., though.
I'm not a good singer, but at this point have been the "lead singer" in my main band for 16 years now. I have made some incremental progress through trial and error, and simply singing as much as I can, both in the context of my main band, doing backing vocals in other bands, and for that matter just singing in the car or at home with recorded music.
After getting throat cancer almost two years ago, I have had to somewhat re-teach myself, and find my "new voice," which is simply part of finding my "new normal," a process almost all people who've gone through treatment for big C have to do. In some ways I actually like my "(post-)cancer voice" better than before, but I'm very fortunate that I'm "singing" punk rock and roll where gravel can be considered a plus rather than a minus. Normally I'd attribute this opinion to my admittedly oversized ego, but people at shows have said the same, so I know it's not entirely my imagination, haha. Additionally, when we were in the studio late last year, on one of our (relatively) "mellower" numbers I tried to sing in my "old" voice, like a more "normal person," and our record company A&R guy (in the booth) would have none of it, haha!
Not everyone can be a great, or even good, singer. However, almost everyone can become a better singer.
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