Domain names must first be registered in your name before you can point it to the server where your website files exist.
Purple Dog offer domain name registration - just visit here to check if your preferred domain name is available or not.
You can search across a wide variety of domain name extensions or TLDs to see if your preferred name is available.
Domain names are not expensive, so you should consider registering several in order to protect your name space and prevent someone registering your brand / company / product name first (known as cyber squatting).
There's not much you can do if someone already has your preferred domain. The only thing you can really do is apporach them to see if they wish to sell it.
Get in touch with us if you'd more assistance on this point.