Once you've found a house you like, you must make a written offer to buy it. Exactly what form that offer should take depends on what state you live in.
In some states, the standard offer is a bare-bones statement that "I'll take the house for $X," after which the seller writes up a draft contract. In other states, your offer must be so complete that the seller could sign it and you'd have a contract right there.
The advertised price of a house is just a starting point. It's up to you (and the market) to decide how much the house is really worth -- whether more, less, or exactly the offer price -- based on such factors as:
After considering all these factors, you may decide to bid thousands of dollars less -- or more -- than the seller is asking for. You'll need to be strategic here. Obviously, you don't want to overpay. But offering too low a price on the mistaken theory that the seller will come back and negotiate for more could result in you losing the house to another buyer or insulting the seller to the point where he or she refuses to negotiate.
Real estate offers almost always contain contingencies -- events that must happen within a certain amount of time (such as 30 days) in order for the deal to become final. For example, you may want to make your offer contingent on your qualifying for financing, the house's passing certain physical inspections (see Nolo's article Getting a Home Inspection), or your ability to sell your existing house first.
The seller may also add contingencies to the offer, such as a condition that he or she have found another house to buy before closing the sale to you.
For more information on your options when it comes to contingencies, see Nolo's article Contingencies to Include in Your House Purchase Contract.
For a detailed analysis of how to decide the right price for a house, craft an offer tailor-made to your and the seller's needs and interests, and negotiate the final contract, see Nolo's Essential Guide to Buying Your First Home, by Ilona Bray, Alayna Schroeder, and Marcia Stewart.