From simply listening for the leak to spraying the mattress with soapy water and looking for bubbles to more extreme tests like submerging the mattress in a tub or swimming pool, the many tests for find a leak in your air mattress are detailed in 5 Ways to Locate a Leak in an Air Mattress. However, the most reliable methods seem to be the easiest: using your ears and spraying the mattress with soapy water. Whichever method you choose, always inspect the mattress systematically.  First inspect the valves. Then, check the seams. Finally, inspect the flat surfaces of mattress. Use a permanent marker or a piece of masking tape.  For “flocked” (fuzzy) mattresses, use fine grit sandpaper or an emery board to smooth the area before attempting to patch it. Be gentle! And make sure to remove any debris with a damp cloth or vacuum cleaner before proceeding.  Alternatively, use acetone—an ingredient found in many nail polish removers—to smooth the flocked area before patching it. Wet a cotton ball with a small amount of acetone and dab the area around the hole. Then, use something rigid like a spoon to scrape away the flocking. Finally, use rubbing alcohol to clean the area thoroughly. Use hair dryer to speed up the process. Or let the mattress air-dry overnight. 
Find the leak. Mark the leak. Dry the mattress completely. Deflate the mattress.