This is an awkward one to answer. This depends on whether or not it has a polished surface and what type of veneer it is. Also what core that the venner is pressed onto.
Usually its mdf and maybe lipped with timber lippings or veneered edgings. If it has lippings and these have shrunk with water damage then its best to get one remade as it will be too bad to press or glue down.
If its a small area then you must clean gently away the splinters / excess glue etc and ensure a clean surface for re gluing. If its a small area then use contact adhesive. Coat both sides with this glue and let both dry (keep both well apart).
Thereafter gently press down the veneer with outward movements to ensure you don't trap any air or bubbles. Rub down using a very smooth sanded piece of timber. Veneer experts use a brass veneer tool.
Should this be a large panel then I'd most likely advise you to find a local veneerer that would be able to make new panels and polish to suit your old one.
I hope that helps and give us a call if you need any further advice.
Yours
Judith Ennis
BASICALLY DOORS
Tel 01200 445749
sales@basicallydoors.co.uk
www.basicallydoors.co.uk
Judith Ennis, June 2008
edit
I can answer this question...
How do I fix the peeling veneer on my kitchen units caused by heat?