Yes, you should put drain holes in the bottom of the trays; the soil needs good drainage to allow oxygen to reach the roots. The soil needs to be damp but not wet.

Don't know what kind of plastic trays you have, but some plastics will crack or break if you try to drill holes through it. I usually burn the holes through using an old soldering iron, but of course anything hot enough would work as wall.

As for what to cover the trays with, keep in mind that the only purpose of covering the trays is to prevent the soil from drying out too quickly. If you're home all the time and can make sure the soil stays slightly damp, you really don't need to cover the trays at all. In fact, in my opinion, it's better if you can get by without covers. If you work all day and can't watch the plants close enough, then you might be better off covering the trays with something that would let the light in (glass, clear plastic, or even Saran or Handi Wrap).

Hope this helps,

Art

Since it is already planted, rather than drilling you can use a hot nail, solder iron, woodburner iron, etc. to melt small holes in the bottom of the tray.

Dave