To get the felting started, all you need is some hot water and some agitation. For small projects like a swatch, you can easily felt in the sink. If you have a bigger project to felt, you might want to try using a bucket or wash basin, or even your bathtub, though that would take a lot of water.
Fill your receptacle of choice with enough hot water to comfortably cover your soon-to-be-felted item as you swish it around, but not so much that you'll splash the whole room with water.
Add a few drops of dishwashing liquid (not laundry soap) to help open up the fibers and make your piece more receptive to felting.
Use your hand or a stick to swish the piece around in the water. Use your knuckles for added oomph, and rub the piece along the bottom of the sink to get a little more agitation action.
Wearing rubber gloves not only protects your hands while you do this, it can also add an extra bit of roughness if you have gloves with slightly textured palms.