Using scissors, cut off the fins. Exercise particular caution with the dorsal fin as some fish have sharp ones (as pictured in the illustration below).
Once you've cut off the fins, it's time to remove the scales. Run the knife or fish scale along against the grain (from the tail towards the head). This is the messiest part of the process and best done in the sink. Once complete, check to make sure you removed all of the scales by running your hand from the fish's tail towards the head. It should feel smooth.
Make an incision along the bottom of the fish up to where the gills connect. You can choose to cut all the way through to the head or stop right at the gills. In this illustration I stopped right at the gills.
Using scissors, remove the gills by cutting on each end. With small fish, these can often be pulled out by hand.