Do I leave the plug in the bottom of the livewell and keep my pump running? Never used it first tourny Saturday lol

Well, it will eventually fill up the livewell and then start filling up your boat so keep an eye on it . 

The brand of boat makes a difference.  My old Champion 206 would overflow if I closed the live well and kept the aerator on.  My Nitro Z20 doesn’t.

There should be an overflow in the side of livewell that wil drain the water out of the boat.  Some livewell of this type also use a lenght of pipe that you can insert where the plug goes and that drains the water when it get high enough.

It's a 1998 express the livewell has a hole in th bottom with a removable plug. It runs out the back of the boat. Do I cut the pump on and leave that drain open or close that drain and just full the livewell ?

You should have a stand pipe.