I have had my eye on a domain for a while now. It will expire tomorrow. If the owner doesn't renew, how long before it will be available for sale so that I can buy it?

The entire length of time will vary depending upon the current registrar. Usually it will be at least 30 days but no more than 45 days. Then it goes into a redemption period of 30 days and the Pending delete status which follows the 30 day redemption period and lasts up to 5 days. In this entire process if the current registrant fails to renew the domain then the domain will be available to re-register.