When a domain name expires, it slips into Renewal Grace Period during which current registrant of the domain name can renew the expired domain name. This period varies for each registrar & domain extensions.
At the end of Renewal Grace Period, domain name slips into Redemption Period. During this period, domain name can be restored and renewed by current registrant by paying redemption fees in addition to the standard renewal fees.
Expired domain name might be put up for public auction by sponsoring registrar. You can participate and possibly aquire the domain name by placing a bid on it.
If domain name is not renewed, restored or purchased through auction, at end of Redemption Period, it will be queued for deletion by registry and subsequently released. Once it is released, you can register the domain name through us.