The complexity of this task is directly proportional to the complexity of two things:
1) Did the expiring domain get any hits?
2) Will it be immediately repurposed by another party?
If the domain got hits, then it will continue to get hits for as long as links to it are out there. As time passes, fewer hits should be expected. (Un)fortunately, you will probably never know for how long this continues, as you won't have the domain anymore.
If someone else buys the domain, and mounts a site behind it, then they will get those hits and you can't do anything about it.
If it's not too much trouble, you should, perhaps, register it for one more year, and help the search engines and your link partners migrate to the domain you're saving by including a "301 redirect" to push visitors/spiders over to the "good" domain. The engines will update their listings with the "good" domain, and start dropping their listings for the "bad" domain, should there be any.
Do this search in Google and Yahoo, at least:
site:expiringdomain.com
That should give you an idea of how widespread the domain is in those engines. If it's nowhere to be found, you're good to go. If it's plentiful, then IMHO you should take the "301 redirect" route until they are gone.
We have also seen that some old domains are stranded in the global DNS system, so that domains that aren't even ours (or expired domains) are still coming to our sites. We put a little script in all of our headers to detect these mis-hits and post a "domain no longer exists" message. We do this because we don't want to diminish the trust people might have in our REAL sites when they hit an unrelated domain by accident.
Hope that helps ...
(Do a search in these forums for "301 redirect" to get the step-by-step methods for your server configuration.)
