manage multiple domains on wordpress

Ive struggled for hours with this and before i struggle any longer, i thought id ask and make sure what i want to do is dooable.
I have created a site hosted by hostgator and installed wp no problem. However, i have offered to assist some tradesmen and create them a basic site for their trade. Therefore, i have purchased another domain and hosting from a different host (godaddy) and cannot work out how to create a new site on wordpress. Do i need to install wp for each domain? Should i have stuck to the same host for the new site?
I am a complete beginner to this and have given myself the mammoth task of helping out a few friends by giving them a small, basic presence on the net, as at the minute, they have none.
Help, please