Well, the drop process is typically about 45 days past expiration. However, you also have to understand when a domain name drops, its unlikely that you'll be able to hand register it, if its any good.
Places like Snap and Pool specialize in grabbing these domain names as soon as they drop and auction them off. Services like GoDaddy offer backordering, but its simply not as effective. Now, also consider that GoDaddy and many other registrars already have situations worked out, where the domains go to auction before there dropped.
For example GoDaddy (GoDaddy,WildWestDomains,BlueRazor) sends its domains to TDNAM.com, where they are auctioned off. If someone buys them, after teh redemption period is over it will go to the auction winner. If its redeemed by the original owner, then the auction is voided.
So - the process is going to vary depending on which registrar the domain is at.
Justin