Negotiations, inspection, appraisal and crossing your fingers
Once you make your serious offer, the negotiations start. The sellers will either accept your offer or counter it. If they counter, you'll either accept their counter or make your own counter.
When (or if) you eventually agree on a price, you'll begin the parade of experts. An inspector will look over the house and let you know about any problems. You'll then decide if you want the seller to fix anything (or everything), and the seller will let you know if they're willing to fix anything (or everything) you're asking for.
In addition to the inspection, an appraiser will come in and determine the value of the home. If it appraises for less than the loan amount you're approved for, you could end up with a problem because you probably can't borrow more than the home is worth. The hope, though, is that it appraises for at least the price you've agreed on with the seller. (If not, you need to go looking for another lender, renegotiate the price, or get the rest of the money from a rich uncle.)