How do you get your own domain and set up your website?
As Shudarshan said, I'd also recommend GoDaddy. Most of the time they have a deal where you can get a domain for a year for only $1, which is a good deal. Once you have a domain, you'll also need to have your own web server that'll host your website and direct its traffic. You'll have to set up proper routing for your domain name and DNS so that it'll direct to that web server, which will allow people to use that domain name to access your website. You can set up the routing on your domain name from GoDaddy's web portal easily enough. Do you already have a server going?
Visit godaddy you can find here