How to increase the height of a wooden cabinet?
Jack brings up a good point, you can create height in both directions. If you want to add height to the top, the process of selecting the method of construction would be determined by the look or style you're trying to achieve. If, for example, you want a Greene and Greene look, the riser might have a pinned finger joint like so:



If you want something a bit more reclaimed looking, maybe you could build a rough box to create your height and then wrap it in rusted sheet metal. 

If a more classical look is desired, turn to architecture. This picture shows a cabinet with what's called a frieze between the crown moulding and the top of the cabinet. This is called Greek revival because it's based on the buildings of ancient Greece .
Note the small moulding below that conceals the joint between the frieze and the case.

In any case the methodology for affixing the top to the riser and riser to the case would be similar.


Assemble your riser in whatever fashion you choose and add some ribs that delineate the opening for your lift.

This is overkill but you get the idea, which is to give yourself more places for attachment points and to create a chase for your lift to pass through.
Lay the completed riser on the case and mark out where the perimeter and ribs will be when assembled. Set the riser aside and pre-drill the lid of your case.
Pocket screw (and glue if you wish) the riser to the top. If you don't have a Kreg jig for pocket screwing, L-brackets will work.
Set the top/riser sub assembly on the case making sure to orient it in the same way it was when you marked out for your holes.
Run screws up through the pre-drilled holes into your riser. You may want to pilot holes into your riser depending on what materials you're using.


Hope this helps, good luck!