However, keep in mind that this can take a lot of work. Learning to sing on your own may require more work than working your voice with singing lessons or private singing tutorials. It's a lot like yoga or self-disciplined sports. You always have to develop patience, inner mental strength, breathing technique through listening to yourself, feeling yourself, and a good vocalist, because you have to approach all that even with a mentor.
I highly recommend Berklee Vocal for Performance with Donna McElroy DVD, and then some practice, and then some silence, and then some listening, and rinsing and repeating. Working to learn to sing for yourself can be a challenge; after all, you don't have a voice instructor to help you see when you make mistakes. Of course, not everyone has the budget or the desire to seek in-person instruction. So can anyone learn to sing? YES, as long as you're willing to work and have realistic goals, you'll be amazed at what you can achieve.
In my professional opinion, as long as you don't have any medical problems affecting your voice, you can learn to sing period. As a singing teacher who teaches singing lessons for beginners, I have worked with many students who taught themselves in the beginning. Then look for a comfortable note at the bottom of your range (test C3 for boys and G3 for girls) and sing the first note in the word “one”. And while singing lessons are the best way to improve your voice, the Internet has made learning to sing for free easier than ever.
Place your hand on the back of your head and sing a very high note in a vowel “ooh” as in “ups”. Even if you're on a tight budget, there are plenty of completely free singing resources on the Internet: many singers have free YouTube videos where they teach singing techniques and even offer sample singing lessons. So if you can't afford private lessons right now, learning to sing online is one of the best ways to start. If you mean learning how the voice physically works and understanding the anatomy, physiology and physics behind it, or learning music theory skills with books, then yes, that is also possible, although it is probably quite difficult, time-consuming and possibly expensive if you want to buy textbooks and other materials.
For example, when you sing a scale, you might want to work on briefly playing a note higher than you're comfortable with before going down the scale again. And you'll be surprised that just using a little bit of this spoiled sound can help you achieve high notes with a lot of vocal power. If you want to learn to sing, practice singing a series of vowels, letting your voice come from the diaphragm or deep in your chest. Now, sing the note again and, as you sing, press on the stomach with your fingers as if you were getting into your stomach.
That's because learning to sing in tune requires you to get feedback on whether you're in the note or not.