Well, you probably don't want to actually make sounds, so here are two exercises that will help without that:
Sit up. There should be a vertical line running through your head, neck, chest, and butt. (your spine is supposed to curve, so let that happen naturally).
I've been taught to use "yoga breaths" while singing--that is, keep your chest high, and take deep breaths, such that the only moving part of your body is your stomach. At the same time, make sure that your airway is completely relaxed, without any tension. If in the off chance you are alone in a sound-proof room, you can take that opportunity to practice singing with these breaths and without tensing up. It's hard to do!
I should probably clarify that these exercises were taught to me for the purpose of learning how to sing in a choir. If you're trying to sing in a death-metal band, it might not be for you, and you should probably wait for more applicable advice.
Also, some more exercises:
The idea is to avoid glottal strokes (this video explains a glottal stop; a glottal stroke is the same concept, but at the beginning of the sound formation.
). To do this, waste air. Take a deep yoga breath, and establish airflow across your vocal cords before letting them vibrate. I tend to relate this to using the clutch on a stick-shift car.
Opera singers, especially basses, have a crazily dark vocal quality. How do they do this? They increase their vocal resonance by increasing their pharyngeal space. To put it simply nearly to the point of incorrectness, the pharynx is the back of your throat, starting from about where the roof of your mouth goes squishy. You can consciously raise the squishy roof of your mouth (a.k.a. your soft palate) and drop the base of your tongue to increase the resonance of your voice. It requires some fairly infrequently used muscles, so you'll have to build some musculature.