Hi Chrissy. Typically, as a buyer of a house that is in a potential short sale situation, you would have signed a "short sale addendum" at the time of the offer. When the owner of the house accepts the offer, you then have a contract which is contingent upon third party approval (the owner's lien holder). The buyer's appraisal is typically not ordered until, and unless, the lien holder formally agrees to the short sale and sets the time frame for their approval. After appraisal, inspection, survey and buyer loan approval, closing can take place within the lien holder's outlined approval period (or later if an extension is agreed upon).
However, your seller could also be involved in the Home Affordable Foreclosure Alternative (HAFA), a Federally subsidized program which became effective in April 5, 2009 (August 1, 2009 for Fannie Mae/Freddie Mac owned loans) and provided a more stream-lined short sale process. If it is a HAFA short sale, the owner's lien holder would have completed an appraisal and set a pre-listed price they would accept at the time the property was initially listed for sale. Then there are very defined time-lines for the lien holder to complete their review and approval of a new buyer and the sale should be completed much faster than a typical short sale transaction. Your lender would also more than likely require their own appraisal to be completed during this process.
Hopefully you're working with a real estate professional who can keep you informed all the way through this process. Good luck on your property purchase!