It is actually quite simple. You have to separate the parts.
Select the bottom gear using the shifter or releasing the cable.
With the pinch bolt loose lightly pull on the cable with your fingers or a pliers click thru all the gears. Make sure each one is smooth.and the cable feeds in cleanly. Pull on the cable and click thru all the gears again the other way. and the cable should pull back out smoothly. If you can don't unseat the cables pull thru the cable adjuster on the derailleur. Nothing should move but the cable. Every movement at one end should be mirrored at the other end.
If that is good it's cable tension.
Is it running good in the bottom gear with no cable tension?
If not adjust with the limit screw.
​​​​​​Take the weight of the screw by pushing the derailleur in. Small turns.
​​​​​​If it is OK wind In the barrel adjuster all the way and back 1 turn.
Pull the cable tight and tighten the pinch bolt.
1 click on the shifter. Wind out the barrel adjuster till it shifts to the selected gear. Or in if you need.
1 more click on the shifter. Adjust if nessecary
Now it's a matter fine tuning.
Run up to the other limit screw. Check it. Push on the derailleur to be sure.
If you can't get enough tension on the cable wind in the adjuster again and pull harder on the cable. or push the derailleur in and then tighten the bolt.
Go slow and it's easy. Watch it move.