Start by removing as much of the excess paint from the roller as possible. Roll the paint onto newspapers or cardboard -- something you can dispose of. Try to use as much of the paint in the roller on the wall you are painting.
Latex paint is easier to remove than oil paint. Fill a bucket with soapy warm water and dip the roller into the water, squeezing the paint from the roller. Repeat several times until the soapy water runs clear. Squeeze the roller in paper towels to remove excess moisture and seal in a plastic bag.
Removing oil-based paints requires paint thinner, which has a strong odor. Wash the paint roller in paint thinner, then wash in warm water and squeeze as much water from the roller as possible. Store in a plastic bag.
If you are going to use the roller within the next 24 hours, squeeze the excess paint from the roller on a disposable surface and tightly seal it in a plastic bag. This will keep the paint roller moist and ready to use.