I just moved to a new house, so when I set up my washer and dryer the washing machine will fill up with water, but the water won't drain. I've taken the hose out of the wall and lower it and the water pours out... is there some kind of pump that I need to activate to get the washing machine to drain? Please help!

You don't need to activate the pump, but you must make sure it is not jammed or clogged with something. Since water pours out when you lower the hose, it sounds like the pump is not turning vs. clogged up. There are two reasons for it not turning:

A foreign object has jammed the pump
The drive belt is broken or loose

Either one is fairly major for a DIYer, but it can be done. Once you get the pump exposed, you can immediately see if the belt is broken. If not, you'll have to remove the pump.

Good luck,
WallyH