Pay those people no mind. (Except me and MASS)
How big is the burn? If it's the whole hand, you should be at the ER by now, or at least
the Doc In A Box.
Smaller, say up to 3 inches across, no big deal...
It's a little late to run cool water over it. If it ever happens again, this is the first thing. Even
'too late', it feels good. Cool, not cold, and don't use ice.
Keep it covered. Do not put butter, mayo or other folk-remedy food-sauces on it. (There
really are well-meaning people who say this. They are what we like to call 'dumb'.)
Plain gauze tends to stick to burns, but you can get non-stick pads.
Keep it clean. Don't scrub hard, but use mild antibacterial soap and water as needed.
If/when blisters burst, let them drain, wash gently, cover 'em back up. Standard medical
advice is NOT to pop them yourself, but they tend to burst on their own. The pocket is
an infection hazard, so you may have to peel a little dead skin.