Needle felting is easy and addictive, but it is also dangerous! Those needles are barbed and they hurt like something else when you accidentally pierce yourself. Felting a flat image makes this less likely than felting a 3D object, so I recommend starting with this technique when you're learning needle felting.
Place the fabric on top of your thick foam piece. Tear off a piece of the wool roving and start stabbing it into the fabric. Because the needle is barbed and the wool fibers are crimped, stabbing them repeatedly will cause the fibers to grab onto each other and shrink together (think of what happens when you throw a wool sweater in the wash!)
So just start stabbing around the shape that you want until the entire space is filled in. You can add more roving and cut excess away as needed.
The wool is going to go all the way through the fabric and stick into the foam. Just gently peel them apart and trim down the excess wool on the back of the fabric.