I would not recommend spray adhesive except for paper backed veneer. For raw veneer (wood through and through) I'd recommend a glue (maybe PVA) and pressing the veneer in some fashion, such as a vacuum bag.
Also, paper backed veneer is mostly used in architectural applications and is almost never used on furniture.
But Tony is talking about shop made veneer, which is raw veneer. I'd saw as thin as you can, sand it after gluing it down and keep your fingers crossed. My experience is that veneer is not strong enough to buckle when glued well to a good substrate but you never know. A hard, non-creeping glue like urea formaldehyde might be best.
MDF is a good substrate and, yes, you should veneer both sides. Just use some cheap commercial veneer on the back, and finish both sides.
[Some additional thoughts: Modern commercial veneer is 1/42". It used to be 1/28". Our ancestors had to hand saw their veneer and it was a lot thicker than 1/28" and they attached it to boards with hide glue and it lasted for centuries. MDF is a better substrate than mahogany boards, for example. It's more stable.]
Last edited by Mike Henderson; 02-07-2010 at 02:49 PM.
Go into the world and do well. But more importantly, go into the world and do good.