Adjusting a rear derailleur is easy if you proceed in a logical order assuming your derailleur hanger is aligned. Put your chain in the middle ring and let’s have a go…

With your shifter clicked to the highest gear, release the cable fixing bolt of the rear derailleur. This lets the derailleur to move to the smallest cog, and lets you set the high limit screw. Adjust the high limit screw so that the top pulley of the derailleur lines up with the smallest cog. Next, move the pedals forward and listen for any clicking coming from the chain – you want to adjust the high limit screw so it is backed out as far as possible with the chain still riding silently on the smallest cog. This allows the derailleur to sit a hair to the outside of the cassette without the chain jumping, giving a quicker upshift into your tallest gear.

Pull the cable taught and tighten down the cable fixing bolt. Give the pedals a whirl and make sure the chain still rides along the small cog relatively quiet without jumping up or off the cassette.

Assuming the cable is taught and well lubed, your shift indexing should be pretty well setup. Don’t worry about it right now too much, as long as one click makes the chain at least want to move up one cog, two clicks two cogs and etc. Click click click your way to the largest cog and adjust the low limit screw so that the derailleur cannot shift the chain past the large cog and into the spokes. You want the chain to freely shift up to the largest cog, just not off of the back of it.

Indexing… Go back to the smallest cog and check that one click up moves the chain up one cog, and one click down goes back. Is the derailleur not shifting up a cog without hesitation? Back out the barrel adjuster a bit. Overshooting the second cog? Screw the adjuster back in. Do the same for the upper most cogs, and then check your work throughout the whole gear range.

If the cables are clean and not kinked and the shifter and derailleur not damaged yet your indexing only works for about half the cassette with a given adjustment, your hanger is likely out of alignment.