I am in the process of building a new desk for myself. I have already built two drawers that will function as the legs of the desk, and I have the tabletop itself. Now, what would be the best way to attatch the flat tabletop to the flat top of the two drawers,without visible screws?
Another simple variation might be to use dowels to secure the drawer to the top. Of course this only works in the planar directions.
If the top is heavy enough it might work as is. But you can reinforce it by using a very small amount of construction adhesive to just keep them together. Then you can still disassemble with relative ease.
A relatively unattractive method would be to use small right-angle brackets. You could also attach a cleat to the sides of the drawer assembly, driving screws into the drawer assembly horizontally and into the desktop vertically. Less unattractive that way. The more expensive and more sophisticated method would be to use a pocket hole drill jig: Lowes Pocket Hole Drill Jig which would require sufficient thickness of wood in the drawer assembly sides.
There are ramifications to each of these methods depending on your restrictions regarding visible screws. Even a simpler method of drilling into the desktop, fastening vertically, then installing a plug and refinishing the surface will mean screws that are not seen, but may not meet your requirements overall.
If all you want is for the tabletop to be secure to the drawers, I would just use a bead of construction adhesive around the top of each drawer unit. Downside of this is it won't be easily disassembled later.
If you need it to be removable, I would use small angle brackets and short screws that are normally used to secure a countertop to cabinets. An alternative to this, and slightly more complicated, is to use ball-head screws and cam locks, these are commonly used in "flat pack" type furniture, you have a screw that is attached to the countertop, and this sits inside a hole in the lower support that has a cam that is turned to pull the top tight with the lower supports.