So I bought a new Schwinn bike to replace my old one that got stolen, and on the first set of gears (the ones connected to the pedals) the cable wasn't taught enough to switch gears. So, I researched, and found that the cable had to be tighter. So I thightened it. Now it goes up to 3 from the first gear, but it won't go down to the 2nd gear. So I turned the dial to one, and it went to one. It won't go to the second gear even though the dial says it is. What should I adjust to fix this? I ride long distances, and up bridges, so this is kind of a big problem.
When the front derailleur shifts in toward the small chainring the only thing that makes it move is spring tension pullino on the cable (as you release it by shifting the lever). If it is not moving easily but eventually gets to the small chainring it's not adjustment. Most likely the cable is not sliding through the housing, due to kinks, broken cable strands or lack of lubrication.
When the front derailleur shifts in toward the small chainring the only thing that makes it move is spring tension pulling on the cable (as you release tension on the cable by shifting the lever). If the derailleur is not moving easily but eventually gets to the small chainring it's not adjustment. Most likely the cable is not sliding through the housing, due to kinks, broken cable strands or lack of lubrication.
Check the tutorial and follow the steps. Most likely it the cable tension is too high, but it might be other things (gummed up / broken shifter, whatever, hard to tell). And mostly it is easier to start all over after having messed up the adjustments...
Again - it may seem to you that it is moving smoothly, but you have to use some logic and thought here. There is no adjustment for the middle chainwheel. The derailleur position is totally dependent on the cable adjustment. If the cable has enough slack to allow the shift to the smallest chainwheel but it does not move when the shift lever releases only slightly to shift to 2nd, then the only cause must be resistance/friction that is impeding the movement (unless something unusual is happening with the lever or there is an interference in the front derailleur pivot that only affects the middle position - either of which would be very rare). It simply cannot be cable tension (which is really cable length), as the derailleur reaches the small chainwheel.
Try this - Shift to the small chainwheel with the lever. Use a rag over the exposed part of the front shift cable that is next to the frame and pull on it as you shift to the largest chainwheel. Now let up slightly and see if you can shift to the middle chainring. If it works that's a strong indication that friction in the upper shift housing is the problem. If it's still stubborn then the lower section of housing may have a problem.
A second thing you can do is to shift 1st to the largest chainwheel and then move the shift lever to 2. Now "pluck" the exposed cable - pull slightly and let go. If it now shifts to the middle chainwheel that is another indicator that the cable is being hung up inside the housing. What you are doing is pulling it through with your hand instead of relying on the derailleur spring.
Frankly, the symptoms are so typical of cable friction that I would simply advise pulling the cable (sometimes one can do so without detaching the end) and lubricate it with a light oil (not grease) while checking for corrosion, kinks and broken strands.