Theres a couple of ways to make a contact form work..
easiest is to just pass the contents of the form to your visitors eMail client and have it sent this way. I tend to call these "mailto forms" - like described here: http://webdesign.about.com/od/forms/a/aa072699mailto.htm ( or google "Mailto form" for more tutorials on this topic). However, mailto forms are very "basic", not all visitors can use them, and are often considered downright unprofessional.
The "proper" way to handle forms is to use a scripting language like PHP or ASP and have the server process and send the form content. This, unfortunately, does require a web server that is capable of running script files - and either obtaining a premade script to do so, or a fair bit of programming experience in whatever script language you choose to write your own,
Most hosting companies will provide you with a script to use for your contact form and have instructions how to use it, so you might want to ask your provider first. If that doesn't get you anywhere, seems like the current formmailer script of choice here on the board seems to be dbmasters formm@iler, which can be found here: http://www.dbmasters.net/node/19 . (or google "form mailer script" to find dozends of others).