Here's an example of how a furniture component
might be built up for veneered work. Obviously different components will need different arrangements, but this example illustrates many of the general principles.
This is a side apron for a desk. The overall thickness needed to come in at 50.0mm to
exactly match the leg thickness, so the ply core was built up to about 42mm then hand planed and taken through a drum sander to get it absolutely flat and to a finished thickness of 41mm. It's then skinned on both sides with 3mm MR MDF.
Next a very thick bottom lipping is applied, this needed to be thick to accommodate a curve in the bottom of the apron. The lipping is flushed off so it's absolutely flush with the MDF.
Next saw cut veneers are applied (if you look closely in the photo you can see the veneer runs
over the bottom lipping) and then flushed off, taking particular care at the top as another lipping is then applied (the top lipping) and then that is flushed off with the side veneers. This illustrates one of the advantages of making your own saw cut veneers, the lippings and the veneer all taken from the same boards, so you're guaranteed a perfect colour and grain match.
This is an off-cut from the finished component blank which is being used to work out the final arrangement for the joinery that will attach the apron to the leg, I seem to remember I squeezed in one more loose tenon and a tiny 4mm dowel to make the final joint rock solid and prevent any risk of gaps opening up in future years.