First off you should definitely go to the foot doctor if you can. They'll do it properly. But if you need it done fast (like in the parking lot so you can keep skiing for the day), do this:
Get a safety pin or some type of needle. Stick it in a flame until it's red hot then push it through your nail and squeeze all the disgusting fluid out. The trick is to melt through the nail more than push through it. Don't go too far or else you'll puncture the skin underneath and bleed more. Every time I've done it the pain goes away the second you drain all the blood and shit that's under your toenail.
Don't use a fucking drill. You will go too far. If you go to the foot doctor they have a special drill and bit to drain the hematoma. Definitely do that if you can manage it.