In the process of domain name registration you lease a domain name for a specified period of time. During this this time you are the "owner" of domain and you can use it for your own needs. In the meantime, this domain can not be used or registered by anyone else, because each domain is unique and can not be repeated.
The registration process is very easy:
Enter desired domain name in order form and click on "Check domain". If the domain that you entered is not registered, the wizard will notify you and you will be able to proceed with registration. Once you have completed the process, you will get an invoice in a few minutes to your e-mail address. Once invoice will be paid, your domain will be registered.
In the case when the wizard reports that the domain is already registered, this domain can not be registered and you will need to find another domain name.