how do you get your own domain name and how much does it cost?

More detail to my earlier reply.
Don't mention your 'name' to anybody and don't post it online. R-click your desktop, select new, select text document. Name it and hit enter.
Write down any domain name you'd like to register. Leave the extension, .com, .tv, .net, etc, off. Make it a single column list. Write down variations. Use Gooogle's keyword tool for assistance.
At most any registrar, you can register or just check up to 500 names at a time. Be aware though, the evidence seems to show that some will take your wish list and register the names themselves to resell at a premium price.
In a few seconds, you will find out which possibilities are or aren't available.
You do not have to register any you don't want. Delete them. Or just select the 'One' you want and register it.
If you use my site, Domain Sales Zone, hover your pointer over 'Domain Names' for a moment to see the drop-down menu. Select 'Bulk Registration'. Copy and Paste your list in the box. Select the extensions you want to consider, enter the 4 digit code, hit 'Enter'.
A simple phone call to my support staff will get you a live person to walk you throught the process if you need help. If you're enterprising enough, it will take you about 5 minutes to find MY phone number and I can walk you through it myself.

 

I stupidly got my domain name through my host, and as a result i dont have access to my cpanel etc. Also I am worried that because my host has registered my domain name will this present problems in the future, can they take the domain name away from me? I really dont have a clue about these things, all i know is that I want control over my own domain name and also over my cpanel. Does anyone have any advice? Any advice would be greatly appreciated! Thanks Lucy x

 

"can they take the domain name away from me?" Possibly.
You can get it from them for a price, I'm sure.