When you purchase a bank owned property that's listed in the MLS, the process is pretty much like buying any other house, except that many banks also have their own addenda that they insist of becoming part of the purchase agreement and the addenda can contain terms that are extremely favorable to the banks.
The banks usually try to sell their properties through the MLS first and if the house does not sell within 6-12 months, they hand them over to auctioneers. When you buy at one of those auctions at which the auctioneers sell huge blocks of bank owned properties, you usually have the opportunity to inspect the properties prior to the auction as the auction houses will hold the homes open for a couple of weekends prior to the auction date.
Whether or not the former owner has a right to redeem the property depends on how the property was foreclosed. If it was done by way of judicial foreclosure, the owner will have a right to redeem and how much time the owner has to redeem will vary (typically 3-12 months after the foreclosure sale). If the property was foreclosed via trustee sale, there's usually no right of redemption. I hope this helps.
Your safest way would be through an experienced real estate agent. Real estate agents know how to research properties, they have attorneys they work with. You have to make sure title work is complete, the closing attorney's office can take care of that part. My suggestion would be to find an agent that has worked with foreclosure properties recently and knows the market. Agents also have the information you will need for contractors when repairs are necessary. Inspections should be made prior to an offer if possible. Some agents have contractors that will look at the property to make sure it's structurally sound at no cost to you if you use them for the other repairs that come up. There are a lot of stories out there of buyers purchasing foreclosure properties and loosing money because they thought they could get a deal and make money. Be careful.
There are some things you need to know prior to bidding on a bankowned property. You should have your inspections prior to bidding, once the bank accepts you offer there is no renegotiating the price and in most cases tha bank may let you have 7 days for an inspction, but it is for your knowledge, the offer can not be contingent upon a satisfactory inspection as teh bank wont accept contingincies in their offers. The property is bought as is, so know what you are getting into. make sure your deposit is at least 1% of the sales price and in the form of certified funds, make sure you include a pre approval letter with your offer. Be ready to close in 30 days from bank acceptance and lastly dont ask the bank to fix anything or put any contingincies in your offer. Most importantle dont try to change anything on the bank addendums, it will cause your offer to be rejected. Good Luck.