Heya! Some people make a little rack for the plants to sit on in the tent and then you can pull out the water tray and empty. People have also used mops and shot vacs. I personally use a shot Vac in my flower tent to keep humidity down.
In the veg tent I let the water sit in the water trays to help with humidity, however my pots are not sitting in the water. Pots should always be raised up to avoid sitting in the water.
Another good idea would to use a piece of plastic or plywood the size of your tent, have it angled down to a drain or something for you to empty.
Cheers,