Carpenter checks runout on a special fixture. Most of us don't have this luxury, but it's still a good idea to check the main shaft as best you can to make sure it hasn't become oil starved and warped from heat.
Thoroughly lubricate the main shaft and reinstall all the components in the reverse order that they were removed.
The brass synchronizers slide into position on collars that are cut on an angle. They should ride with approximately 0.050 inch of space between the synchronizer teeth. If there is less clearance, or especially if they touch, then there is too much wear and the synchronizer should be replaced.
Set the cluster gear in position and slide the cluster shaft into place.
This key prevents the cluster shaft from sliding out of the case. It is held in position once the midplate is bolted up.
Next, you can slide the main shaft back into position.
Now is a good time to make sure all the sliders still move into their positions easily with no catches.