I know this is a noob question...

I’ve been using blender for awhile. There’s a story behind this: I’m attending UAT.edu for two different degrees: Game Art & 3D Animation. I couldn’t even think about affording autodesk or maya. I talked to my professor and he pointed me towards blender. “Free?” I thought! This must be too good to be true! Yet I’m constantly amazed by the things blender can do!
My question is this: I have way too many vertices taking up precious computer space. How do I get rid of the unecessary vertices without destroying my model? I know there’s a shortcut but I don’t want to search through my portable hardrive looking for the right video. Could someone help me out here? I will in return post the picture I’ve been working on for my friend’s band as soon as it’s done. Thanks in advance - PortzMonkey