You don't pee out the liquid you drink. The kidneys act as a filter for blood and one of their most important jobs is maintaining the right amount of water vs. saltiness in your body. Too much saltiness is bad, and too much water is bad. If you have too much water, the kidneys will produce more-watery pee.

Pee is yellow because of the chemical urobilin. People will say urea is responsible, but this is not true. Urea is the main component of urine (pee) but has no color. The color is urobilin. If your kidneys decide you have too much water, then your urine becomes more watery and this dilutes the urobilin, reducing the yellowness of the urine. Similarly, if you do not have much water at all, then the urobilin will be highly concentrated giving a dark yellow/orange color.

If your pee is red, you almost certainly are peeing blood, which means something very bad is happening in your kidneys or bladder. Pee can rarely be other colors - if your pee is green, your kidneys are filtering something blueish into the urine stream, etc. This is not necessarily a bad thing.