Tuning up and re-aligning your brakes is pretty easy. This will reduce wear on your brake pads, reduce squealing, and make the lever easier to pull. There are two main steps, realigning the brake pads and adjusting the tension in the brake cable.

To make this a little bit easier, there's a picture with all the terms you need to know about brakes to take full advantage of this tutorial.

You will need:
-Hex wrenches
-You will probably need 5mm, but sometimes you will need 4mm or even 3mm
-10mm wrench
-Phillips head screwdriver

Note: If you have a multi-tool meant for bikes you will most likely have the needed hex wrenches and the screwdriver.

Step 1: Adjusting Your Brakes

First you need to figure out if you brakes need to be readjusted.

Your brake pads are out of alignment if
1. When the lever is pulled, the bottom of the brake pad is below the rim (sometimes you can see this from the other side of the fim)
2. If the brake pad ever rubs against the tire
3. If the brakes are skewed so that they touch in the back
4. Generally if the brakes look "off" or skewed

If your brakes rub without pulling the lever then they may need to be adjusted (especially if they look skewed) or you may just need to adjust the tension (see step #4).
If your brakes squeal you also want to do a slight readjustment but do not need to fully readjust. In this case see step #3.

Step 2: Aligning Brakes With the Rim

You want to get your brake pads lined up along your rim so that they are in the middle of the rim and tilted slightly forward.

To adjust your brake pads you will probably need a 5 mm hex wrench and a 10 mm wrench, or something very close to that.

You want to stick the 5mm hex wrench in the front part of the brake. This is either a bolt or a notch that fits a hex wrench. You will be using it to control and adjust your movements. You then want to put on the 10 mm on the bolt on the back of the brake calipers.

By turning the 10mm wrench counter clockwise you will loosen the pads and be able to adjust them. You can use your 5mm wrench for small delicate movements and your fingers for larger movement. In addition, it is helpful if you loosen the back bolt just a bit so that it is a little difficult to move the pad. This will allow you to have finer, more accurate adjustments. When you are done adjusting, retighten the nut. Make sure it is very tight and doesn't move if you try to move the brake pad. You will probably need to adjust multiple times to get the brake pads correctly lined up.

Your brake pads are correctly aligned if when the brake lever is pressed the bike pad does not hit the tire and does not fall off the bottom of the rim. It should be as central as possible, but you don't need to spend hours getting this perfect.

Step 3: Aligning Brake Pads Cont.

If you look down at your brake pads (lever unpressed) the pads should be flat or slightly forward. If they are tilted slightly back, then you need to use the wrenches again to readjust.

Keeping your brake pads flat or tilted forward will work and not cause wear. If you often get squealing brakes (or want to prevent this) you want to tilt your pads slightly forward.

There are two ways to do this.
1. Significantly loosen the nut on the brake calipers to loosen the brake pads. Readjust by them by pushing the front slightly in towards the tire with your fingers. You need to still keep the brake pads aligned in the middle of the rim. Use very small movements.
2. Losen the back nut very slightly so the brake pad barely moves and put a rubber band around the back of the brake pad. Tug the rubber band out (see picture) until the front is just slightly tilted in. You may need to losen the nut a little more if this doesn't work the first time. You can also use two rubber bands to get more force.

Step 4: Adjusting Tension

Adjusting the tension is helpful as it ensures both your brake pads hit at the same time (so one side doesn't wear out too fast) and the brake lever feels right when it is pressed. That is, you don't have to pull to hard or barely at all for the brakes to engage, you can find the medium between.
First we will adjust the tension in the springs holding the brakes together.
Most brakes have a small spring inside of the brake post. The tension in this spring determines how quickly your brake swings back after it's pulled in. The most important part though is to have the tensions in the springs the same of both of the brakes so that the brake pads hit at the same time.
To adjust this part you will need a phillips head screwdriver.

First look down at the brakes from above while you press and release the brake lever. Find which ever slide is slower at reacting and work on that side.
When you tighten the screw, the tension of that brake increases, the brake pad moves out, and this side will react slower. In contrast, if you screw the screw out, the tension decreases and the brake pad moves in.
On the slower side, try screwing the screw in. You want to use small motions, only turn about a quarter of a turn, when you adjust this screw. If one screw is screwed in all the way, loosen it and tighten down the other side.

When you have the tension correctly adjusting the brake pads will hit at the same time when the lever is pulled and the brakes should look about even looking from the front.

If you are unable to adjust the tension without the brakes rubbing, try readjusting the brake pads so they are more flat. You can also loosen the tension in the brake cable (see step #5)

Note: Most road bikes have slightly different brakes usually called caliper brakes that do not have the screw on the side. For this system, there is a spring at the top of the brakes in the back that controls the tension of each side. You need to adjust this spring (by moving the sides up or down) to adjust which side hits first.

Step 5: Adjusting Tension in the Brake Cable

The last thing you want to do is adjust the tension of the brake cable. This is the cable that goes from your handlebars to your brakes.
As mentioned before, adjusting this tension will get the feel of your brakes right. Ideally you want to be able to pull the brake lever in so that it is about 1 in from your handlebar and parallel to the bar.

If your cable is very loose or very tight, you first want to adjust it down by your brakes. Loosen the bolt and let some cable out to make them looser, or pull some cable in to make them tighter. Sometimes this is easiest to do by keeping the cable steady and pushing in or out on the brakes to move where the bolt is placed. Make small movements in this adjustment as a small amount of cable will create a big difference in how the brakes feel.

Once you have the brakes pretty close to the right feel you want to use the barrel adjuster for the brakes. This is on your handlebars where the brake cable meets the brake lever. This piece has a lock nut on the outside, so to make any adjustments you first need to screw that open, about 1 full turn, to be able to move the rest of the barrel.
A barrel adjuster changes the length of the housing the cable has to fit through. If you screw the barrel adjuster out, the housing around the cable is effectively longer, the brakes will get closer to the rim, and you will have to pull less to engage the brakes. In contrast loosening the barrel adjuster makes the cable more slack, moves the brakes farther from the rim, and forces you to pull more to engage the brakes.
Thus you want to screw the barrel adjuster in or out depending on what adjustment you are trying to get.
You do not want the barrel adjuster to be too far out. If it looks too much like the picture above, screw it all the way in and tighten down the cable with the bolt on the brake calipers.
If you have the opposite problem, you screw the barrel adjuster all the way in and you brakes are not loose enough, loosen the cable on the calipers.

Note: If you have toed your brakes significantly or have lower quality parts, you may not get this adjustment with the brake lever parallel to the handlebar. You can either toe your brakes slightly less or you can settle for letting your brake lever come in a little more. Just make sure you can't pull the lever so far that it bottoms out and hits the handlebars.

Note: You can also just adjust to feel. Road bikers usually keep their brakes much tighter so they engage quicker than other bikes