How do I set up CiviCRM?
CiviCRM needs to be hosted on a webserver that meets the proper hosting specs. See http://book.civicrm.org/user/getting-prepared/hosting/

Technically you could host it on your own computer, this would not be practical for an organization.

I believe that your CiviCRM installation should be hosted where your website is hosted.

Depending on the size of your database (how many contacts) and which features of CiviCRM you would be using (civimail, civicase, civicontribute etc...) the current hosting for you website might not be adequate.  For example, many commodity hosting companies that offer shared hosting cannot really support CiviCRM.

Your best bet for learning about hot to setup civicrm is on the wiki, or in the book http://book.civicrm.org/user/initial-set-up/installation-and-basic-setup/

If you have never installed a web application on a server, though, I would urge you to speak with the vendor who built/supports your website, or the company that hosts it, or find a vendor that specializes in CiviCRM.  Installing CiviCRM is not like installing an app on your phone or computer.