I freeze my hands from time to time when I have injured fingers. Dave McCleod calls it freeze therapy. It works marvelously except 30 minutes of finger in ice bucket is a kind of hard. See his video
I have been massaging my hands, forearms and feet. The result is amazing. It takes stiffness out and increases range of motion. It feels amazing especially after a good night sleep.
You need to use oil. Nothing special just vegetable oil. Dry massage does not work.
I like to have a towel and a pail of warm water. Search self massage in YouTube. Basically you warm the part by rubbing, working it with a combination of thumb, side of your hand or a stick. You work any soreness out. The session should last good amount of time. Wash yourself and wipe off excessive oil. Having oil on you is not all that bad as your skin seems to absorb it.