In Finding Deleted Domains, I talked about using WhoIs.net to search for expired domains, but this is not exactly the best way to get a valueable domain. For a high quality domain, you probably have to go with one the auction services, like Snap.com. You should be prepared to pay more as the bidding process can be quite costly, but cheaper than directly dealing with a domain owner who wants thousands of dollars for their domain name.
Before jumping in with the bidding process, read How to Snatch an Expiring Domain, which is a thorough and interesting look into the way registrars are retaining deleted domains and making it harder for the rest of us to actually catch an expired domain.