I assumed that it was proper to place the ball of my foot on the pedals like in normal bicycling, but in a lot of the videos on Youtube, the riders have the arch of the foot on the pedal. What is the best way, because I’m having my feet slip on the pedals often.
I find it depends on the type of riding. When I’m doing street ,trials, or muni I have the middle of my foot on the pedal so that there’s a stable, sturdy base. When I’m riding xc or distance I’ll use the ball of my foot.
I vary my foot position based on the type of riding. For easy spinning down the road I’ll use a position closer to bicycling with the ball of the foot on the pedal. When doing any kind of hopping or dropping on the unicycle putting the arch of the foot on the pedal feels more secure and there is less of a chance of over-extending the ankle.
What davidp said. For me, that equates to about 99% of the time, balls. 
But for cranking up large or steep uphills, or if you’re doing lots of dropping, moving your feet forward on the pedals takes some strain off the calves, and protects your ankles in the drops.
If you aren’t doing those things though, balls.
I ride with the arch of my foot on the pedal all the time for muni, trials, street and commuting. Mostly a matter of habit, I even do this when I’m on a bike now-a-days.
Does anyone know what the proper foot placement is for freestyle riding?
From vids, it seems to me on riding tricks, they all use the ball.
+1 I read of a guy who forgot to shift his feet from the balls to arch over the pedal axel before a 4 ft. drop and upon landing tore the achilies of his back foot.
at first i rode like my bicycle but started having pain and swallow ankles from dropping so i realized i could absorbe the impact off the fall with movin the pedal to the arch of my feet,
hope this helps!
Definitely balls. Again there are some exceptions for a few specific things but, at the risk of repeating myself again, 99% of the time, balls.
Chauncy, your arch-style riding is going to slow you down. for general riding, you get the maximum mechanical advantage of your legs by centering the ball of the foot over the pedal spindle (and ankling).
I have found the ball position to be of advantage in every situation (I used to be an all arch rider before I visited this forum).
I don’t manage to jump high, so I figured drops are the thing to train the relevant muscles. I have found that placing my balls on the pedals (don’t confuse this with a seat discussion) allows me to pull up my toes and exit a too deep drop in progress by slipping of the pedals.
I’d give it a try with low drops and never without shin guards to see whether that’s good for you. I totally agree, if you do it wrong you will tear something.