If you’re looking to tackle the more advanced stuff in order to keep your ride preforming well, don’t be scared. It’s actually pretty easy. The cool thing about bikes, is that they fall within my DIY rule: I was going to pay to fix it anyway and it won’t cost me any more if I make it worse, so there’s no reason for me to not try and fix it myself. With a little time and patience even I can keep things in good running order on my bike and I was a liberal arts major in college. For the non-engineers like me, here’s a basic intro on how to deal with more challenging bike parts.

Derailleur:

This is the technical term for the mechanism that changes the gears on your bike. The one controlling the crank set–the gears attached to your pedals– is the front derailleur. The one on the cassette–the gears on your back tire– is, not surprisingly, the rear derailleur.  (They may also be referred to as the front and rear mech in online tutorials.) If the gear doesn’t shift right away or you’re shifting off of the chain ring or doesn’t shift with the clicks if you have index shifters, chances are you’re going to want to tune your derailleur. Unless you’re seriously out of alignment, this is actually not terribly hard to do.
The first thing you’ll want to do is check your cable for rust and wear. You’ll also want to clean your chain and all the gears. This maintenance is easiest if you can set up your bike somewhere you can spin the pedals and change the gears. I lock my bike into a trainer, though hanging it from a stand or the ceiling works too. It’s a little hard to hold the rear wheel off the ground, shift gears and spin the pedals at the same time, so being able to suspend the back wheel is key.

If your chain is shifting off of the gears, you’ll want to adjust the limit screws. This determines how far left or right the derailleur shifts. There is a screw for the high gear–labeled “H”– and a screw for the low gear–labelled “L”.  Shift the chain to the respective gear and loosen or tighten the screws as appropriate to change how far the gear moves. On the rear derailleur, the “L” refers to the low gears on the big gear and the “H” refers to the little gear. The inverse is true on the front derailleur, where the “L” stands for the smallest gear and the “H” for the largest gear.
Once you’ve set your limits, you can fine tune how the gears shift by tightening or loosening the barrel adjusters on your derailleur. If you don’t see a barrel adjuster by your derailleur, it may be on the handlebars next to the shifter. As you spin the pedals, click through your gears (or approximate if you have down-tube shifters) and make sure the chain goes from gear to gear without skipping or hesitating. If it does, tweak the barrel adjuster until it shifts smoothly. I found most of this to just be trial and error (predominantly because I’m a hands-on type of learner and my difficulty translating instructions into practice is the reason I wasn’t an engineer).
Derailleur adjustment is covered in more detail on this “How To” page of guru Sheldon Brown’s website.
Brakes:
Brakes are important, so you want to test any adjustment you make in a safe environment before subjecting them to road conditions. Brake failure at speed is really unhelpful. Like the shifting, braking is controlled with cable tension, the tighter the cable the more responsive the brakes. (Disc brakes excluded here. Sorry.) You don’t however want to the brakes so tight that there are no gradients to the braking or the brake pads (called ‘shoes’) are rubbing against the rim of the wheel. Though you can encounter a number of different problems, usually  they have to do with the brakes being too loose or too tight.There are numerous types of brakes and so each fix is different but they generally follow a similar process.
The first thing you’ll want to do is check the brake shoes for wear. If they look worn, check with your LBS about replacing them. Like the derailleurs, brakes also have a barrel adjuster for easily adjusting tension. Tighten or loosen as necessary. If none of the above work, most brakes have a hex bolt holding the wire in place by the wheel. Disengage the brake or remove the wheel, loosen the hex bolt and tighten or loosen the cable as needed. Make sure that the hex bolt is screwed in tightly when you’re done, as it’s not very helpful if the bolt comes loose the first time you brake.

Armed with a simple bike tool (I use the one pictured above) you can do much of the regular maintenance on your bike. There are also numerous online resources to help you keep your bike in top form, but since this is getting pretty long more on that next week.

Photo Credits: Park Tool Sheldon Brown Derailleur Sheldon Brown Brakes