How soon can one secure a web domain when an existing one expiries?

I am planning a website with an unfortunate existing web address. Upon review, I have found that that the domain is expiring soon. So how soon can one register it after it expires or does the existing owner retain use of it indefinitely?

The existing owner has the right to renew the domain name.

Watch the domain, if it actually expires and current owner does not chose to renew, then usually there is a waiting period (how long depends on domain company that registered the domain with original owner) then they will make it available to the general public for purchase.

you can backorder the domain name