Start with the rear derailleur (RD). Shift into high. Loosen the cable clamp and tighten all barrel adjusters all the way in. Adjust the RD high limit screw so the RD pulleys align with the small cog on the wheel. Reattach the cable, pulling hand tight. Try shifting once. Adjust cable tension with the barrel adjuster until it works cleanly. Shift into low gear, then adjust low limit screw to prevent shifting into the spokes. Fine tune barrel adjuster for clean shifting in all gears.

FD is similar, starting in lowest gear and adjust low limit to just prevent chain rub on FD cage. Tighten cable clamp, being sure cable is routed on correct side of clamp. Adjust cable tension so there's no rubbing while in middle chain ring (assuming triple) while shifting through full range on rear. Adjust high limit to prevent shifting off large chain ring.

FIne tune as needed. If this doesn't work, check that the rear wheel has the right number of gears for the shifter--I'm amazed at how often a wheel gets swapped without this simple check.

Many old shifters need a soaking of WD-40 in the indexing mechanism. Many grip shifters are just broken.