First, cut a thin slice off the edge of a block of wood or a board. Cut it as close as the accuracy of your bandsaw will allow, and leave it just barely thicker than needed. Adjust the table to the veneer as is described in "Table Adjustment" above. Run the veneer through the sander, using only your hand to guide it. As it comes through the back side of the sander, begin pulling it out with your other hand. After making one pass, adjust the table approximately 1/4 to 1/2 turn up and sand the opposite side. Keep making fine adjustments and sand alternating sides. If one side has deeper cut marks in it from the bandsaw, you should sand that side more often that the other until the marks are removed. When you get very close to the thickness you desire, run the piece through a few more times with the table set at the same depth. The resulting veneer is very smooth and a very consistant thickness.
If you wish to make several different veneers that should all be exactly the same thickness, it is best to cut them all out in one batch, and run them sequentially through the sander at each table setting. This way, all of the pieces will go through the same process, and when they all go through the sander the last time, they all will have identical thicknesses.
Since grain direction is not a concern with thickness sanding, you can also sand projects with wood pieces glued-up in many grain directions. A popular use for thickness sanding is flattening wooden chess or checkers game boards, which often have the grain of the "checks" alternating. Here at Moritz Designs, we have used the thickness sander extensively for sanding wooden box lids which have been made by gluing up a variety of woods in unique patterns. We also have used a lot of burl veneer and various bandings in box lids, and these are always sent through the sander to level them off and give them a mirror-smooth surface. Since thickness sanding doesn't care about grain orientation, the possibilities are only limited by your imagination, instead of your tools.