How can I install a kitchen drawer with only one side and no front beam?
Undermounts are the standard of the industry these days and most models don't require a side wall to support the drawer. Here's a pdf from Accuride that shows the rear hook you'll need (See page 3, figure 9), although Blum, Hettich, etc. all have there own version. The drawer will have to be made to the specs of the slides you purchase which will mean some rather serious woodworking, a pre-built drawer from a supplier, or you can get a drawer system like this. Good Luck!