Remember that warm-ups are not intended to sound good. In fact, most of them sound rather silly and obnoxious, even if you have a professional singing voice. Find a private place to do your warm-ups if you don't want to disturb others.
Be sure to warm up both the head and chest voice. The head, or upper, voice is breathier and lighter-sounding than the chest, or lower, voice, which is more solid and loud. To find your upper voice, mimic an opera singer. Your lower voice is closer to the range in which you generally speak.
Practice warm-ups that stretch your mouth. Do scales with an “Ooh wee ooh oohweeoohweeohh” sound stretching the corners of your mouth wide. Or practice tongue trills while starting at your highest note and moving down the scale to your lowest.
