In most cases, foreclosed properties will be listed for sale with local real estate agents on the Billings MLS. My experience is that HUD (government loans) foreclosures do offer value in that they seem to be aggressively priced. Homes owned by conventional loan market companies use market appraisals to price the properties and don't seem to be priced as well. Occasionally, we'll gain knowledge of a local bank-owned repo before it hits the market and can make an run at it before it's listed.. that can often lead to savings.
Another way to purchase a repo is to purchase it at the sheriff's sale at the courthouse. Not all foreclosed homes will reach this sale, and many won't sell at the sale. It requires a significant amount of time and energy to stay on top of the sheriff's sale list. If you do purchase a home through this sale, you should expect to have a check in hand without appraisal and to buy the property as/is.
Otherwise, the process for purchasing a repossessed home is the same as purchasing any other home except that the seller is a bank. The bank is as interested in maximizing their profit as any other seller might be. They negotiate differently, and there is clearly a strategy in negotiating with them. A potential downside is that the banks often times want to sell the homes in as/is condition.
Pretty lengthy answer that I hope helps.