Don't do a whois query unless you're going to register the domain immediately. Otherwise you're likely to find that someone else with access to those queries got the domain first. At that point, you will have to either buy the domain, backorder it or pick a different one.
Enter the domain name in the address bar of your browser. If it looks like the site is being using primarily for pay-per-click advertising, then it is more likely that the domain will be released at some future date than if the domain name is being actively used by a business, organization or other entity. In fact, if the domain has already expired those ads may have been put there by the registrar.
If you made the mistake of searching for available domain names on a web site and the domain got snatched up by someone else before you registered it, then it will probably be over two years before it expires and gets released.
If you are willing to spend at least $200, try to make an offer on a domain name. You can make an offer on any domain, not just ones that are listed.
There are some sites where you can backorder a domain name on a first come, first served basis, rather than a highest-bid auction format. If you backorder there as soon as possible, the domain can no longer be backordered by anyone else through that site or any other site that uses the same interface and back end.
If the domain goes past its expiration date without renewal, go to the auction site(s) and join the auction for the expired domain. Most domains will initially go up for auction on just one site, depending on which one the registrar has an exclusive partnership with. Many of the better domains, especially two-word ".com" domains, get snatched back up at this point, before they are ever "deleted" where they can be caught by a backorder request.