Are there simple ways to construct shelving under a kitchen worktable?
it is somewhat difficult to answer because I cannot tell what is easy for you.  It depends a lot of what kind of tools you have.

One way I can think of requiring basic tools would be to cut 3 pieces of 2x4 to fit between the legs and attach them to the leg with screws.  They are horizontally placed about 12” below your table top.  Then cut the shelf and have it rest on top of the 3 pieces of wood.  Attach the shelf it support with wood glue.