Improving iMac speed with external hard drive

Hello, I am the owner of a 2 GHz Intel Core 2 Duo iMac, and after having it a while and having a hard drive the size of (less than) 250GB, I am running out of space and the computer performance is taking a hit. So I picked up a 1TB external hard drive.

I'm not too big on computer speak, so in simplest terms: Is there any way I can move stuff onto there that will improve the speed of my computer without totally messing things up? In theory I want to run off of the external hard drive, but I'm afraid I'll mess things up if I just cut and paste everything onto it.

Can anyone shed any light on the situation?