Dip it in the water, so it is thoroughly wet, and get it all soapy. Work it gently between your hands for a few minutes, until it is completely wet and soapy.
Repeat this 2-3 times until the ball is completely covered by the wool, with fibers going in all directions.
Keep working it between your hands- rolling, squeezing, etc. Keep the ball very wet and somewhat soapy too. As it starts to felt, the wool will shrink and become firmer, and you can work it harder. Rolling it on a bamboo mat or any other ridged surface will help felt it when it gets to this stage. Keep working it until you can't separate the fibers from the surface of the ball anymore.
During a class we discovered that if you dip the felt ball directly in very hot water as you work (using a slotted spoon), the process goes much faster. Heat helps the felting.
If you want to make a ball entirely of felt, the process is the same but you neet to start with a tiny wad of wool and keep felting it and adding more layers until the ball is the size you want.
I use cheaper white wool for the inside of the ball, and colored wool for the final layer. You can also make a "geode" using different colored layers of wool. After it is dry, slice it open with a sharp knife to reveal the layered effect.
This is a lot of (very messy) fun. My cats have been playing with these balls for years now, and have yet to come anywhere near destroying them. The one with the bell as a core rattles nicely, and they are especially fond of it.