Well, I'm repairing my brother's cheapo acoustic g**tar. We decided to use new Gotoh tuning pegs, instead of the one's already broken (even cheaper tuners). So I had to enlarge the tuning peg holes on the headstock and had some chips while drilling.
We decided to apply a Walnut burl veneer to hide those imperfections. But I have never glued a veneer before and search function, didn't give me the answer.

Well here is my question:
How should I apply the veneer over the headstock? I removed the paint till the bare wood. I'm planning to use Bison wood glue (don't have the access to special Veneer glues). Should I cut the veneer exactly to the shape of the headstock and apply it? Or should I cut it with some parts remaining in excess, glue it to headstock and trim the edges (in excess)? What is your experience?
Thanks in advance..

Or should I cut it with some parts remaining in excess, glue it to headstock and trim the edges (in excess)?

That's it. Put the glue on the headstock, not the veneer, the veneer will curl up if you do that and will be harder to install. once you've pressed the venner on the headstock cover it with a flat piece of wood to give some pressure to it and clamp that on at least 3 - 4 places. Make sure you've got either cling wrap or wax paper between the veneer and your clamping wood so it doesn't stick to the veneer (glue seeps through the veneer and glues your clamping wood to it)

Thanks for the answer Phil!