I know from antiquing all the time you come across a lot of great wood pieces that have water damage or chipped veneer. This will usually turn off most collectors/buyers but don’t let it intimidate you. If something catches your eye you should really consider buying it and repairing the surface. The surface damage actually gives you the power to haggle more and get the piece for very cheap in some cases.
Depending on the kind of wood veneer you buy it can be relatively cheap to expensive. There are a vast array of woods to choose from and the grains can blow your mind. Usually the more exotic wood veneers have to be special ordered through a specialty wood dealer. I don’t think you will find veneer at Lowes or Home Depot but I could be wrong. I purchased a 4×8 sheet of Teak veneer (around $200, but I have a lot left over for other projects) from a dealer in Sacramento California to restore the surface of my Seeburg Jukebox pictured below. The original surface of the veneer on this cabinet was not in the best shape.
Something to remember is that you always want to cut the veneer to overhang the piece of wood you are applying it to. This gives you room for error in case it does not line up appropriately. The surfaces that you are going to apply the glue to need to be completely free of debris otherwise you will see it when the two pieces are glued together. Here are a few things to use to help complete the job:
Here is a video from DIY to show how simple it is to veneer something and trust me it really isn’t difficult.