On a preforeclosure, you're either talking about a short sale (if the value of the house isn't enough to repay the mortgage and other expenses of selling), or simply a purchase (if there's sufficient equity to cover amounts owed).
Let's take a short sale. Person owes $500,000, but the house is only worth $450,000, and the person can't afford to sell his house and come up with an additional $50,000 in cash...plus the commission...plus back interest, penalties, etc. In that case, you make an offer. Maybe $450,000...maybe $350,000. Doesn't matter. The lender has a short sale "package"--a number of items that must be completed by the seller. Often, it includes a couple of years of past income tax returns, a listing of assets and liabilities, a requirement for a "hardship letter," and more. Your offer is one component of the entire package. The package--your contract, hardship letter, tax returns, etc.--is sent to the lender, who decides whether to eat the loss and allow you to purchase the property. It can be a long and uncertain process.
Now, if there's enough equity in the property, the process is much different. To use the same basic example, let's say the house is worth $450,000, and the owner owes $200,000. But maybe the owner lost his job and couldn't make the payments...or he got sick...or he bought another house thinking he could sell the old one. You get the idea. So the owner owes $200,000, plus back payments, penalties, attorneys fees, etc. Let's say the grand total is $230,000. Make an offer for any number between $450,000 and $230,000. Say $300,000. It's just like a normal purchase. $230,000 of that would go to pay off the existing mortgage, plus back payments, penalties, etc. Then, if there's a real estate agent, there'd be the agent's commission. Whatever's left--$70,000 minus commission, if there is one--would go to the owner. And you'd have bought a $450,000 house for $300,000.
In the case where there's equity in the property, the question is whether the seller will accept your offer. At one extreme, the seller may want to hold out for the full $450,000, or close to that. A lot of them do. Many of those do get foreclosed upon. At the other extreme, some investors buy the house for just what's owed on it--in our example, $230,000. Or, some investors will acquire the house doing a "subject to." The owner in preforeclosure deeds the property over to the investor, who promises to clear up any arrearages and to continue making the payments on the property. The mortgage itself remains in the seller's name, although the property itself is now owned by the investor. The investor's out-of-pocket cost, in this example, is the $30,000 it takes to clear up the arrearages and bring the mortgage current. The investor may give the seller some additional cash. At some point in the future, the investor sells the property and the $200,000 mortgage is paid off. The investor keeps the remainder.
Certain states--Maryland, for instance--has laws governing purchases of properties in certain states of pre-foreclosure. Make sure you're in compliance with those laws, if your state has them.