My domain expired and now it's registered by someone else. How do I get my domain name back?
Also see HelpDesk article: Get a domain that is owned by somebody else.
If your domain expired and was deleted from the registry, technically it is no longer your domain. It was dropped and became available for anyone to register as a new name. In this case, it is not appropriate to file a domain dispute (see article: Domain Disputes / changing ownership of domains), which is applicable only when a domain has been fraudulently transferred to another registrar.
You can contact the current registrant to see if they are interested in selling the domain to you. Many times they have purchased the domain, but perhaps they do not have any plans for using it. To find out who is the current owner of a domain you can use a whois search, such as whois.com or who.is.
You may want to consider registering a new name with an alternate spelling (or add "site" to the end for example). Or perhaps a different extension would meet your needs, such as .biz or .info.
It is important to understand that once a domain expires and drops into the available pool of domains, anyone can register the domain as a new name. You are no longer the current registrant, and you may not have any rights to the domain even if you were the previous registrant.