The lender you are using to get a mortgage from will not accept an appraisal ordered by the homebuyer - there are strict compliance guidelines which stipulate who exactly can order the appraisal and depending on who is ordering it what process they have to go through. The compliance guidelines preclude the homebuyer/borrower from ordering an appraisal and it being able to be used.
However if you need to get an appraisal because of another reason, you would want to seek out appraisers in the local area to the property. If the loan officer (which is what I am) was still able to order the appraisals individually from appraisers, what I personally would do is go to http://local.yahoo.com/
and enter in "real estate appraisers" and punch in the address of the property - this should generate a list of appraisers who are close in proximity to the property which will increase the likelihood they will be familiar with the property's immediate area neighborhoods and the home values there. You will want to interview several, as there are all sorts of different personalities and types of appraisers, and feel free to ask them as many questions as you can think of like how much it cost, how long will it take, how long they've been doing appraisals, how familiar with the neighborhood they are, etc. (write a bunch of questions down ahead of time and write down their answers). For another appraiser database, you can use the FHA approved appraiser roster at https://entp.hud.gov/idapp/html/apprlook.cfm
but it does not have their contact information and sometimes the address listed isn't exactly where they are at... so you still have to use another source to find each appraiser's contact information by using the information on the FHA appraiser roster.