If I have a website hosted on a site, how do I set up a custom domain name? If I have a hosted blog or whatever and want the adress to be somethingsomething.com, how would I go about it? What do I do after purchasing the domain name?
Basically, the website that you have purchased your domain from will have its own manager that you can login to. Go there, and point your nameserver(s) to where your website is being hosted. You can find out what the nameservers are from the control panel of your webhosting service. After you have updated the nameservers for your domain, go back to your webhosting service and add the name of your domain to the list of domains. Give it 24 hours, and then your domain will recognize itself belong to the new server now.
Are you planning on paying for it or do you want it for free? If you want to pay I would recomend Godaddy.com and if you want it for free, use dot.tk