The glue usually used for constructing and repairing wooden instruments is hide glue. It used to be a bit tricky to use because it came in granular form and you had to melt it in a double boiler and use it within a certain time. Fortunately, it's now available premixed in plastic bottles just like regular white household glue and carpenter's glue. It's should be available at any well-stocked hardware or home center store.   

The advantage of hide glue is that it releases at a relatively low heat so future repairs can be done more easily. If your first repair attempt doesn't do well, just heat up the glue joints with a blow dryer, take the thing apart, clean it up a little and do it again.