Simplex.

If it is a Simplex, then the correct way to adjust it is to set the D/T lever all the way forward with the cable loosened at the derailleur. Adjust the inner stop with the cable loose. The inside plate of the derailleur chain guide(cage) should be ~1/16-1/8" away from the chain with the chain on the small chainring/large cog. It may be helpful to rotate the derailleur body on the frame tube so that the front of the derailleur cage is toed in slightly. Or you can just use a set of needle nose pliers to bend in the front of the outer cage plate slightly. Since the shift from the large chainring to the small chainring is done entirely by spring action, this will facilitate a smoother shift.

After you get the inside stop adjusted, tighten the cable and the cable anchor bolt. Shift the chain onto the small cog in the rear. While pedaling, shift the to large chainring by pulling back on the lever. Set the spacing of the outside derailleur cage plate so that it is ~1/16-1/8" away from the chain. This is accomplished by loosening a small bolt on the cage that secures it to the horizontal rod. You can move the cage on the horizontal rod to set the outer limit. You can also rotate the cage on the rod so that the bottom of the outside plate is roughly concentric with the circle of the chainring. Do no over tighten this bolt when you retighten it! After you set the outer limit, it will be necessary to go back to the inner limit and recheck it. You may have to go back and forth a few times to get if right.

This is not a precision unit.

Remember when you are riding to let off pressure on the pedals slightly when you are shifting in the front.