You know how sometimes your gears don’t change with firm frankness? When they don’t snap into action like German watch works or have the precision of the pistons in an F1? Or even when they react like the voice automated system that understands “Constitution Hall” as “Congressional Balls”?
If this is the case, you may need to check your derailleurs.
As with anything, this complex procedure gets easier to figure out with time and practice.
So let’s go through the steps.
You’re going to want to start with the chain on the smallest chainring and on the largest freewheel cog. This will keep the tension on the gear cable loose so that you can do your adjustments. If the cable is too tight, you can relax the tension at the anchor bolt, where the cable ends. Check and see where the inner plate of your cage is. It should be 2mm from the chain and that can be adjusted by the mount bolt. Your gears will shift crisply if the tension is right. If the chain hesitates, give the barrel adjuster a twist or two. If it has a hard time passing to the smaller chainring or doesn’t drop at all, you’ve got too much tension.
Look for the limit screws, which are two screws sitting side by side horizontally. In some cases, they may be labeled “High” and “Low”. In the likelihood that they are not, press your finger onto the cage and slightly unscrew the screws. Whichever makes the derailleur move towards the bike is the “Low”. This screw affects the changes when the chain goes down the rings. The “High” affects the chain as it goes up the chainrings.
Make changes with the barrel adjuster first. If that doesn’t work, try the limit screws.