Full dentures. Ideally take them out at night. If you do so, gently clean them with an old toothbrush or denture brush. Never use toothpaste with it, only water or if you have stains, then soap. Do not store them in water, leave them out dry. To clean them, once a week while you shower or bathe, let them sit in a glass of water with a couple of drops of white vinegar.
Partial dentures. Same cleaning regimen applies, except that it is important to remove them before you brush your teeth and it is ideal to not wear them when sleeping.