Here's how to glue a crack shut so it'll be stronger than the surrounding wood.
My African folding chair cracked lengthwise.
I fixed it with epoxy thickened with wood dust. That's usually the best thing, but use whatever you've got. Even Elmer's school glue is okay if the crack isn't separated too far.
If you're fixing a valuable musical instrument talk to a luthier about glues. They'll suck you into a glue-filled time-vortex.
Step 1: Clean the Injury
This crack happened to be an old glue joint,. So I needed to remove or at least scuff the remaining glue so the new glue would stick.
I pried the crack apart and sanded as high in the crack as I could. Then I pushed the crack together to sand the outer part.
Step 2: Glue in the Joint
My favorite adhesive is "EPOX-635414" epoxy from http://www.uscomposites.com
Get the metering pumps "EPX-P41" that go with the jugs.
Follow the directions!
After that I mixed in an equal quantity of wood dust from my beltsander to thicken it.
I was doing some boat work and already had some mixed up. By the time I got to the chair the glue was getting thick. I used a pencil to wedge the crack apart. I whittled a wooden lath into a chisel shape and used that to trowel glue into the joint.
Step 3: Work It In
It was cold out and my glue was thick, so I moved the sides of the crack around to help get the glue into the joint. If the whole thing had broken off that would have made life easy, but the other half of the joint was epoxied already from a previous session.
Step 4: Clamp It
You want to see glue squeezing out of the joint. That's called "good squeezout" in the trade.
I'm using bar clamps because I have them. If you don't have clamps use innertubes, sticks, wedges, or weights to do it.
Step 5: Clean the Excess
If all you care about is strength you'll leave some squeezout on the joint. As the glue soaks in it'll be drawn back in. Otherwise you can get a "starved joint" and less than maximum strength.
I'm cleaning off the squeezout cuz I want it to look like it's not there. After I can see the edges clearly I bang on the sides a little to get them to line up better. If your sides slide around too much you can put in a dowel or a temporary nail.
Step 6: Put It Someplace Warm
Then I stood it in the sun to get warm and cure faster.
I forgot it there overnight and it rained, but oh well.
When the glue was hard I took the clamps off and it was as good as new.