I used to be a drum major. There are two ways to spin a baton or mace with one hand.
The first is when your holding it in your right hand and spinning it clockwise. Start it with the grip palm down and rotate as far as you can clockwise and let it go on the fatty part of your palm just under your thumb. As it moves on your wrist, turn your hand so that it stays on top. When it gets to the pinky side of your grab it again. You'll see that when you get back to the first position (palm down), the mace/baton will be the opposite direction. This will make it so that it never goes towards the end.
The other way to spin a baton/mace is to spin it counterclockwise. To do this, grab it as close to center as possible, then gripping it palm down, start to spin it counter clockwise. When it spins about a quarter of a turn, let it go. Quickly turn your hand and catch it on your fingers.
Note: As this gets faster, you'll want to move a little to the right of center to increase the speed and a little left to decrease the speed. This is more difficult than the easier spin above, but with practice both are easy enough to master.
Also cheerleaders batons are different and they do finger twirling instead of hand spinning. Its very difficult to do hand spinning on a cheerleader baton because of the lighter weight.