There are three kinds of adhesives that work best on wood. Polyvinyl resin glue, or white glue, works for china, paper, and wood, but it's not waterproof. Neither is aliphatic resin glue (or carpenter's glue), which is quick-drying and stronger than white glue. For outside, there's resorcinol—formaldehyde glue. It's waterproof and good for doors, windows, and moldings.
For more on tools, consider:
How To: Clamp a Glue Joint
7 Essential Woodworking Glues
Quick Tip: Working with Wood Glue