When you say vocal timbre, you probably are referring to resonance. I agree with the above posts that a good coach is your best bet, but I can guide you in the right direction with a couple of simple exercises.
In order to increase your resonance, you need to move your vocalizations into your soft palate. If your voice sounds thin to you, I can guess that you're vocalizing in your nasal cavity, and not using any power. Another difficulty some novice singers have is too much of a "chest" voice when they're moving into upper registers. This is a result of trying to shape their throat to emulate a richer sound, but ends up causing an artificial, "clenched" sound.
The exercise is a five-note, descending scale, like this: 5 - 5 - 5 - 5 - 5 - 4 - 3 - 2 - 1. Start on a comfortable note for you, and upon completion of each scale, move up a half-step. However, this is NOT an exercise to increase your range (as your vocalization should change as you reach your passaggio), so when it becomes uncomfortable, change direction and begin working back down a half-step at a time.
Now, this is the important part, but difficult to describe in words. The way this is sung is, "nung, nung, nung, nung, nawh-awh-awh-awh-awhng." You should hear the change in your timbre, or resonance, when this is done correctly. Feel your soft palate flexing and "closing off" the ng sound at the end of each note with an "ng" ending. Breathe correctly as well, and do each scale in a single breath. Do not lift your shoulders when you breathe -- you should see your stomach move outward when you are breathing correctly.
Be sure your tongue is relatively loose and not flexed while doing this. As a matter of fact, a variation on this exercise is to do it while sticking your tongue out your mouth. It won't be as clean-sounding, to be sure, but this will encourage a loosening of tongue pressure as you sing.
Finally, watch yourself in a mirror, and try to shape your mouth into a vertically-shaped "O" as you sing. Imagine the pictures you've seen of Christmas carolers and how artists usually draw their mouths. You can't always shape the mouth this way depending upon the consonants involved, but this will help create the correct embouchure.
Best wishes.
-Bruce
