All expired domains has a certain period within which it can be renewed again. Then it goes into redemption phase, this also has a set time frame, approximately a month or so. If the owner does not get it renewed this time, then it goes to the general availability queue and anyone can book during this time at normal prices.
Alternate method is to approach the owner directly and buy it from them.
I wouldn't bother, there's no guarantee that Google is retaining any of the Authority that the domain has accrued, in fact it's pretty unlikely, plus if you repurpose the site the linking sites might notice and pull their links anyway and you lose the PR.