We have a outside door that the veneer is coming off .

Without seeing the extent of the damage, it is difficult to give you the right answer; but I have in the past, purchased veneer online, and pieced it in to the damaged area. First I removed the loose veneer and squared off the area with a sharp blade. Then I cut the veneer to the exact size and using wood glue, adhered to the damaged area. After its all dry, I gave it a light sand and then painted, stained as desired

Stick it back and clamp it till dry.

http://homeguides.sfgate.com/fix-veneer-door-70376.html

If the veneer is still all there? You can get some exterior glue to reglue it down. Titebond exterior glue the best that I know of for gluing anything outside. If you can’t lift up the veneer very high to get glue under it. Try using a thin putty knife and put glue on both sides of the putty knife and slide it underneath the veneer to try and get a good amount of glue under the veneer. You can also use thin shines of wood to put glue on to slide under vaneer, whatever it takes that you can find to slip under the veneer to put glue on to get it under the veneer will be fine. Glue should still wash off anything like a putty knife long as it’s still wet it should rinse off in water. But read the label to be sure! You’ll either need to take the door off and lay it flat where you can put some weight on top the veneer to make sure it’s pressed down tight to the rest of the wood of the door so the veneer will glue properly back to your door or you will need some clamps and take some wax paper and clamp a board to the veneer to hold the veneer tight to the door while drying. Usually give it no less then a hour to dry if it’s inside the house at room temperature. If outside or colder it will take much longer to dry enough to remove weights or clamps! Again follow directions on the glue!

Another option you can do that may be even easier to solve your problem if the veneer is only loose at the bottom of the door and not loose more then a few inches yet? You can get a piece of metal in different metals design as a kick plate to go on the bottom of your door that you can screw on that will hide that loose venee and keep the veneer from getting any worse then it is now! You can get these metal kick plates at most any home improvement center like Home Depot or maybe Fred Meyers if their in your area? If its only loose at the bottom of your door this may be your simples solution! I also recommend putting a sealer of some type on your door on that outside of the door cause the weather getting thru the veneer and that’s what’s causing your problems you have now. You can use Thompson‘s water seal or whatever exterior finish your home improvement store recommends to protect your door from the weather! The kick plate can be a nice addition to your exterior of your door and nice when your hands are full and you want to push a door open with your foot and not leave foot marks on your door veneer! They come in gold, chrome,stainless steel. Good luck

There might not be anything to stick back on. If that is the case, this will help.

https://www.google.com/search?q=replacing+veneer+on+doors&rlz=1C1BLWB_enUS700US700&source=lnms&tbm=vid&sa=X&ved=0ahUKEwi0vfrPqqPZAhXqrVQKHVKNAPYQ_AUICygC&biw=1422&bih=684&dpr=1.13

I think the kick plate answer will work as the veneer is shredded. thank you for the help