Locate the soft palate. Using either your tongue or the flat of your thumb, first find the hard, bony area commonly referred to as the roof of your mouth. (This is actually only the front portion of the roof of the mouth, also called the hard palate.) Then reach back, beyond and above the hard palate, and find the soft, muscular area in the back of your throat, which is actually the back portion of the roof of the mouth. This is the soft palate.
Open your throat by raising the soft palate. This will provide a larger resonating chamber for your voice, making the sound richer and fuller. Do this by making yourself yawn and noting what it feels like when the back of your throat is completely open and unrestricted. With practice, you'll master widening that space on command without forcing a yawn. Another technique for raising the soft palate is to open your mouth while visualizing and trying to create a smile in the back of your throat.
Practice singing simple sounds with your throat wide open. Do this by singing long, drawn-out vowel sounds on any pitch you'd like. Feel the sensation of your open throat as you sing, making a mental note of that feeling, as you work on learning to reproduce it at will.
Advance to singing one-syllable words that end with consonant sounds, again on any pitch. Be sure to hold out the vowels long enough to feel the open-throat sensation before resolving to the consonant sounds that follow. Keeping the throat open while singing consonants can be tricky since most are formed by closing the lips. So, remember never to hold out consonants, only vowels, and you'll have a much easier time mastering proper soft palate technique and producing a fuller, richer tone.
Continue these exercises daily until opening your throat becomes automatic and doesn't require any real thought. Once you've reached this point, you're free to focus on the quality of the vocal tone produced by your built-in resonating chamber.