Shirley,
To reglue veneer that is delaminating I use Elmer,s carpenter wood glue and an old plastic credit card. Gently work the glue under the separated places and then clamp them down. Clean up the glue that oozes out before it gets totally hard. Once dried it's a good fix.
The pic you posted shows damage that I'd consider minor compared to some I've worked on.
Good luck.
Joe