If it's a domain you wish to own, you should consider using a backordering service in an attempt to grab the name for you, such as GoDaddy who will charge $18.99, or snapnames.com who charge you a minimum bid of $60 which is only payable if you are successful at securing the name. Note that if two people use SnapNames to grab the name, and they do secure it, you will go to auction.
Also bear in mind that many of these services have a pool of registrars where they place the winning name. You may, therefore, also have to pay additional charges to have the name transferred to your preferred provider. The expiration date of the domain would, at the same time as transfer, extend for a year - so you're paying for a renewal rather than a transfer.
If the domain is not a gTLD, then it really depends on the extension. Many ccTLDs also go into a redemption period but not all of them.
Good luck with grabbing your name!
Amos