We found a piece of property where the owners owes back taxes, the owners have moved their mobil home off the property, divorced, and are living else where. The previous owner was sent a notice of deliquent taxes, by a law firm. It was addressed to the owners C/O the previous owner. Can I lay claim to the property if I go and pay the back taxes? Is there a waiting period for me to be able to get a deed? Or would I have to wait for the county to have some kind of auction?

In my State/County the property goes up for auction and the highest bidder wins.

No you can not just go to the court house and pay the taxes, does not work like that.

A few states are stating online bidding, but most have one or two sells a year, and advertise all property that is a specific number of years past due, some do two years many do three years

The bids will start at the tax due plus any costs and fees. Three things can happen,
1. it will sell
2. it will not sell, so it may go into a special status sale next time at no min bid
3. it will not sell and just be sold again at next sale.

**** if it sells, then it is a big difference in states, in one state you may get a special deed that day, you own it. In many others, you get a tax certificate, then you have to wait one to three years to redeem the certificate to get a deed.