How long does it take for domain name after expiring to become available for registration to any one to use?

A lot of registrars have grace periods so people can get back their domain name without the risk of someone else taking it. Apparently, the grace period can be anywhere from a couple of weeks to a full year, so you should check with the registrar to see what their policies are.

Pretty much instantly.

There are nameseller sites which have "waiting lists" of names people want, and as soon as one comes up, they auto-register. They charge for the service, but for something hot it might be worth it.