There are all kinds of veneer out in the world. But here is what I learned:
PSA pressure sensitive adhesive veneer is regular veneer with some nasty nasty 3M adhesive applied to it. You peel the paper off the adhesive and press it down onto your wood. Done. My main complaint with this is that the adhesive has a thickness. It is thick enough that you can see it on the corners after it is applied. It looks like a black stripe on every seam. Oh, and it smells like a the south end of a north bound dead skunk in a toxic waste dump. The smell never seems to go away. Oh, and there are special requirements that the surface be smooth before applying it. Some people say it should be sealed. Too much effort.
The kind of veneer I use is paper backed, or sometimes wood backed. Again it is regular veneer but this time a very thin paper is applied to hold the veneer together. The paper does not make a nasty black line at the seams. But the downside of this veneer is you need to use contact cement to glue it to your project. And contact cement is the devil's spit.
Get whatever species of veneer you want. Walnut, mahogany, rosewood. whatever is normal for your equipment brand. or whatever makes you happy. It can be expensive. And if at all possible look at the grain before you buy. Knot holes are interesting but not appropriate. Get something with some character in the grain so it is easy to tell if you match the grain around the edges. If you can find "figured" walnut it looks super cool. It has patterns that seem to changed in the light.
But I digress. . .
If you plan ahead, lay out your veneer for a couple of days on a flat surface so some of the curl gets worked out of it. That will make the rest of the process less annoying.

Layout your veneer face down on a "safe" surface so you will not damage it. Cut a strip to the correct depth to match your case. Make sure it is long enough to cover the sides and top. The bottom does not need to be covered but I usually cover it anyway because I'm nuts. Veneer can be cut with a box cutter. Just score it and it will break sort of like sheet rock. You have to leave about a quarter to half an inch overlap on every edge because gluing this stuff down is not an exact science. Cut all the lines very square just like you were building the case. This will help lining things up later.

Before you take another breath label each seam in the front corner.

Then put matching labels on your case for each corner. Again, when your veneer, case, eyeglasses, gloves, dog, face, tools are all covered in contact cement, you don't want to be figuring out which corner goes where.

Sand the plywood on your case down to 220 grit. Just enough so it feels nice to the touch. I draw squigle lines with a pencil and then sand those off to know when I have touched all the surfaces. Draw your letters back on when you sand them off. Wipe everything down to remove the dust.
Now you absolutely have to setup two work spaces. One will be for gluing and the other for routering/sanding. Keep them far apart.
Get some contact cement and a "chip" brush. DO NOT get that water based contact cement. It is useless.

If it does not say it will kill you and blow up your garage then get something else.
Get one of the "J" rollers.

Maybe you can live without it but you won't live as well.
Get gloves. This glue is nasty. Have an extra pair handy because you will probably need them once the first pair starts sticking to your dog.
Get acetone. Not turpentine or any other paint thinner. ACETONE. Acetone is a solvent and will remove the contact cement if you spill. And you will spill. It also dries completely with no residue.

Point a reasonable layer of glue on the veneer. HINT: hold the veneer on the case surface when it will be installed when you are painting on the glue to the veneer. It is the perfect way to make sure you are not getting glue from your workbench onto the finished surface of the veneer.
Put a less reasonable layer of glue on the case. I usually put two coats on the case because the glue soaks into the case more than the veneer. It takes about 20 minutes to get tacky.
NOTE:Some of these pictures are from different projects because I'm a failure in some technical things.
Get some dowels. 1/2 inch diameter works fine.You need enough dowels to keep your veneer from touching the case until you have it lined up where you want it. Three is a good number. Contact cement in ENTIRELY UNFORGIVING. If you are doing it right the two surfaces will bond instantly and permanently as soon as they touch. If they don then you waited too long or not long enough.

Line up your veneer so it overhangs every edge of the case. Get it as close to the edge where you want the grain to match up. Make sure it is square. Pull out the middle dowel and press down a point with your hand. You can still move the veneer a tiny bit at this time. Then press down a line all the way across. Then work from the line out to the front and back keeping all the air bubbles out as much as possible. Then use the J roller to really push the surfaces together. Be careful not to roll over the edges and crack the veneer.
Now take your project over to the "dirty" table. Really, no need to wait. I trimmed my veneer right away.

Theoretically you can trim veneer with a knife. I did that on several pairs of speakers. But buy a trim router and get on with your life. You need a flush trim bit with a bottom bearing. 1/2 inch diameter if fine. Adjust the depth so no more that 1/4 inch of the bit is exposed. This will prevent cutting into your case if your router is not perfectly flat on the surface. You will find that one way the router will tend to push the veneer down onto the case and the other way it will pull it up. The cleanest cut is when it pulls it up. There is not much need to worry about "climb cuts" like when you are cutting real wood.
But regardless there will be some paper and a tiny lip of veneer left when you are done. I'm pretty sure the router bits are designed to leave this lip but the paper is just annoying.
