Hey this is Johnny Bravo from Performance Bicycle.
Derailleurs guide the chain from here to gear and when they work they're great but when they don't your stuck and your frustrated, so take deep breath relax, i'll show you how to adjust your gears.
First, a little background derailleur adjustment is dependent on three things:
Derailleur alignment, this is the derailleur's alignment relative to the frame and drivetrain. The rear should hang parallel to the plane of the bike.
Cable tension, this is controlled by barrel adjusters located on the derailleur, the shifters and in the case of road bikes, on the down tube cable housing stops.
Stop or limits screws, these are the two screws on the derailleur body that limit how far the derailleur can swing, to the outside, H for high gear and to the inside, L for low gear. These keep the chain from shifting off the cassette.
Let's get started on your miss-shifting the rear derailleur. Your cable and housing should not be rusted, split or frayed. If there's any problems on the cable does not move freely replace it.
Now check the chain for stiff links (that's what she said) and bends. Turn the cranks backward and watch the chains progress through the pulleys. If you see the cage jump, we have a bad link and/or a bend in the chain. You can try to fix this link by flexing the chains slightly from side to side. If that doesn't work you must replace your chain.
Next check the alignment the chain runs through a cage with the two pulleys. The cage should be parallel to the plane of the bike if it looks bent or it's out of alignment, you need to have your local professional mechanic take a look at it.
Okay your cable and chain are good, what's the next step?
Shift or to the highest gear that's the most upward and smaller cog. At this point you're going to check the high limit screw, H. Look at the pulley cage, it should line up directly under the highest cog. If it's too far outboard, turn the H limits screw clockwise until the pulley cage is correctly aligned. If it is too far in, try unscrewing the H one turn counter clockwise. Did the derailleur move out? Did it align? If it didn't move outboard, the cable is too tight and you'll need to reduce the cable tension. The barrel adjuster on the rear of the derailleur controls cable tension, turn it one turn clockwise.
Did the derailleur move outboard? Aligned? Good! Stand up and pat yourself on the back you're halfway home with the rear derailleur.
Your going to try to shifting to the next cog up, the next biggest one turning. While turning the peddles shift one. Did you make the shift? Is it quiet? Answer yes to both means you can skip ahead to setting the low stops screw.
If the derailleur clatters and clanks when you shift, and doesn't shift, you need to increase cable tension. Turn the barrel adjuster on the back of the derailleur until the cage aligns with that second cog.
Check it again. Good, but noisy? Fine-tune the cable tension to eliminate the noise. Once you've dialed in the highest cogs, the rest should click right into place, so shift up the cassette and make small tension adjustments as necessary. At this point shift up to the lowest cog you're ready to set the low L stops screw.
First take a look at the pulley cage, it should be directly under the lowest cog. If it is, find the L stops screw and tighten it clockwise until the cage just moves then back off one-sixteenth of a turn. Now check it by shifting down one gear and then back up. If the pulley cage is a little outboard unscrewing the L screw should allow it to move the proper alignment. Now we're on the gears. Perfect! Good work.