Every mortgage needs some consideration of value. Your downpayment and the type of property you are buying will determine if and when an appraisal is needed. Virtually all refinances will require an appraisal.
If you put down less than 20%, a mortgage insurer will have their own valuation system. If it fails, then they will order an appraisal at their cost. If a property fails the valuation and there is a concern surrounding the property such as conditions, a private sale, or a foreclosure then a lender may require you to pay for an appraisal as part of your conditions.
If you put more than 20% down, an appraisal will be always be required. Some lenders have internal valuation systems that they will charge a fee. Sometimes lenders will order an appraisal for you and not charge you upfront, but they will add this expense to their closing costs.
As far as the process goes, once you receive an approval from the lender, an appraisal might be one of the conditions required in order to release the funds. At this point, an appraiser will be calling you to set up a time and to collect payment. Based on property type and location, the price is approximately $250-$350 and is the responsibility of the borrower.