Barge Cement is way and above the best thing out there. I was none too thrilled when they "improved" it by making it more environmentally friendly. However the new stuff in the blue tube works quite well and may work as well as the old stuff. I still try to find the yellow tube. It will never let go. It is what shoemakers use.
It is a contact cement that is applied to each side and allowed to dry for about 15 or 20 minutes. One must be very carefull putting the pieces together as once they touch, they're stuck. press the pieces together, pound them with a rubber hammer and your really don't even need stitches...I always do but...
Clean up with acetone.
Dap Weldwood is often touted as being as good. I don't think so. It is much more fluid and moves around. It takes longer to dry both too a tacky surface and then once the piece is stuck it exudes powerful fumes much longer than Barge. That said, it does work well...just not as well as Barge.