I'm happy to share how I do it, but please know I'm no expert at veneering. I've only done one other pair of speakers and through trial and error this is what I settled on
I bought a glue bottle with a roller on the end from Rockler. I don't put glue in it though. I just squirt glue directly on the surface and then spread it with the roller.
As far as the order of construction goes:
I do the inside lip, which you won't see when the grills are attached, first.
Then I do Bottom, Sides and top.
Then the front edges last.
Once glue dries, lay the veneer on the speaker. You can move it around no problem because the glue is dry.
I then put a t-shirt over it and hit it with a hot dry iron.
Then trim using chisel
I have some blocks of hardwood that a glue sandpaper to (spray adhesive). I use that to finish the edges. It's easy to do on the first piece, but takes more finesse once two planes have veneer on them