There are 2 adjustments that can be done without machine work. The end play in the upper shaft is more critical than most people realize. This is the shaft the worm is attached to.
If there is end play in this, you will NEVER get all of the slack out of the system.
The worm rides on 2 tapered roller bearings. There should be a small amount preload on these bearings. To adjust the preload, you put in or take out either shims or gaskets on the bottom end cap. On some cars this can be done in the car but is easier on the bench. The drag link needs to be disconnected for doing this.
If you want to get REALLY technical, in this case a small amount of preload can be defined as 1 to 2 ft. lb. of torque.
The other adjustment is the worm to roller mesh and this should be done with the steering CENTERED and in the car with the car sitting on the ground.. Adjust till there is no felt free play. If the steering wheel will not "bounce" when you bump it slightly, it is too tight. Even with all brand new parts in a rebuilt box, it is sometimes hard to get it exact the first time but it can be had.
These boxes work great for street driven cars. Not so much for racing.
A side note if you are rebuilding one. Try and stay away from off shore parts. The gear heat treating is REALLY POOR.