If you are looking to buy a domain name that is already register you have two options:

1. You contact the existing owner and try to acquire it directly from him. If you agree on price, there's a procedure to be followed for the domain name change of ownership which varies from country to country

2. You wait till the domain name is no longer paid by the existing owner and you purchase it like any other domain, to do this you can check domain name expiry date on various websites and save that alert into your calendar. Bear in mind that different countries are offering a trial period prior to complete deletion time in which the existing owner can still extend the validity of the domain name.