I second the contact cement recommendation: there's two good features, firstly it's not a water-based glue
you want, water expands the veneer and it can crack on drying. Second, it's rubbery, allows local expansion/contraction
to be slightly different between the soft veneer and the underlying rigid or crossgrain substrate.
It's also very quick.
The drawbacks: you can't wash out paint rollers after using them to apply the adhesive, and it's hard to use
brushes; sometimes a card-type glue spreader or rubber roller might work for application.
Final step is the press-in-place, using a slip-out sheet (of masking paper, when I do it) so the
positioning can happen before actually pulling the sheet out and making a very final contact between
the two prepped surfaces.