The glassware or test tubes are placed on triangular pegs, which allow the water to drip onto the tray and then through a tube to the sink.  The rack can be attached to the wall over a sink or mounted on feet.  The 10 mm x 8 mm flexible tube costs less than $6 on Amazon.  A dab of grease on the tube end prevents leaking between the tube and tray.

A similar unit is available from McMaster Carr for $411.

I was too cheap to buy test tubes for the photograph, so printed a large one and small one In PLA.