Here's part two. This was too image-intensive, so some of the images have been converted to links that you need to click. Sorry.
Wire connections
There are a lot of different ways to connect wires, but only a few that will provide years of trouble-free reliability.
In most cases, the best electrical connection can be made by soldering the two wires together, and covering the joint with heat-shrink tubing. Make sure you slide the heat shrink tubing over the wire first, and slide it far enough away that the heat of the soldering won't melt it. When soldered properly, the solder will be drawn THROUGH the copper wire strands. You should apply the heat to the bottom of the wire, and touch the solder to the top. This will allow it to flow all the way through. If you're melting the solder with the tip of the iron, you're not doing it right. The heat of the wire should be what melts the solder.
Another type of connection that is considered adequate is the use of butt-connectors.

Strip approximately 1/4" of wire, stick it in one end, and crimp. Do the same with the other piece of wire. For interior wiring, this is adequate. If you're outside, you want to take additional steps. You want to use a little bit of di-electric grease on the bare wire before inserting into the butt connector, and you should also cover the entire connection with heat-shrink tubing. Make sure you slide the heat shrink over the wire BEFORE you crimp! If the wire is crimped properly, you should be able to tug on it without having the wire pull out.
An alternate to the bullet style connectors is the closed-end connector. You stick 2 pieces of wire in together and crimp one end.
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This style is a bit faster than butt connectors, but takes up more room, and can put strain on the wires if they are pulled tight.
Another alternate is the wire nut.
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These are adequate for TEMPORARY connections, but should not be used permanently. Vibration or tugging on the wire can cause them to come apart.
When you crimp these connectors, the cheap $5 crimpers that you buy in K-mart don't cut it. They only crimp a small part.
This quality pair of Klein crimpers sell for about $25 and are well worth the cost:
Whenever you need to tap off of a current wire without cutting that wire, you can use what's called a "wire tap". There are a couple different varieties. The most common style looks like this:

There are 2 spots for wires to go into. One passes all the way through, which is where the wire you're trying to tap into goes. This won't interrupt the flow of current through the wire. The second spot is where you put the end of the new piece of wire. You then use pliers to push the metal piece down, which connects the two electrically. These are available pretty much everywhere, but are clumsy and not very convienent. The preferred style looks like this:

This pic shows them in the closed position. These pieces clamp right onto an existing wire much like the previous style, except that you don't have to screw with having your 2nd piece of wire lined up. You just clamp this into place, then attach a male disconnect to the other wire. You can then plug them in together. Not only is this easier, but it's easy to unplug later on, and also gives you a good test probe point later on if necessary.
For any type of wiring that you may need to remove, it's always a good idea to use disconnect type terminals. There are many styles, including flat

and bullet

. Both the flat and bullet are available in fully insulated and partially insulated styles. I've only shown the partially insulated style, because they are easier to see. I prefer the fully insulated for obvious reasons, but there are times where the other style can be preferable.
For attaching wires to screw-style terminals on equipment like amplifiers, there are fork style connectors.
When selecting electrical connectors, the color makes a difference. Yellow is for 12-10AWG. Blue is for 16-14AWG and red is for 22-18AWG. Make sure you use the proper size. If you use one that's too big, it won't secure the wire properly.
Grounding
Properly grounding your electrical components is vital if you expect them to perform properly. Whether it's fog lights or a stereo amp, bad grounding can create all sorts of problems.
Rule #1: Location.
The location of your ground is very important for a few reasons, and the type of equipment that you're hooking up will dictate where you're best off putting your ground. For instance, if you're hooking up stereo equipment, you need a ground location that is going to minimize conducted radiation. Conducted radiation is sometimes called a "noisy ground". For example... if you hook your head unit or amplifier ground to the same spot that your directional light circuit is hooked to, every time your directional lights go on and off, you can hear a popping noise in your music. This is because the directional light circuit is an unfiltered circuit that produces stray voltages in the power and ground lines. These stray voltages are "noise". The closer you get to the grounding point of a circuit like that, the more noise your equipment will be susceptable to. So... where do you ground stuff? Well, if you're mounting the amp in the back of the car, stay away from the very back portion where the tail lights and hatch motor are grounded. A better spot would be a little bit farther forward, like above the rear wheel wells. If you're grounding something up front (like the factory head unit) and you find that the factory radio ground isn't sufficient, run the ground over to the passenger kick panel area, or even over to a passenger seat bolt. The driver side kick panel is noisy, as is most of the firewall. A lot of stuff grounds there.
If you're dealing with other equipment, such as lights, you don't have to worry about those things being effected by noise, but you DO have to worry about these things effecting other equipment, like your radio. Generally this isn't an issue because lights get grounded outside, very far away from any stereo grounds. Your primary concern for grounding this type of equipment is simply to find a good spot that will offer a clean electrical path to the chassis. Bumpers can seem like a good ground for your fog lights (well... not on a thirdgen, but stick with me here...), but they aren't. When you ground to a bumper, the electrical path to the chassis is usually through some bumper bolts. Over time they corrode and don't conduct well. Likewise, the point where the lights are grounded to the bumper is usually exposed to the elements and won't take long to corrode. A better choice is to run the ground into the engine bay, and find a clean, dry spot that won't be as susceptable to salt and corrosion.
Rule #2: Make sure the connection is as good as possible
The best location in the world isn't going to help much if you don't actually take the time to make sure the connection is as good as possible. If you don't have a good solid ground, the resistance goes up, and that causes all sorts of problems. With audio equipment, it can result in something called a ground loop, which is what results in alternator whine in your music. With lights and other equipment, if the resistance goes up too high, the equipment just won't work, or even worse, it'll ground through other equipment, which can result in a whole host of odd, unexpected problems that can take forever to track down if you don't check the ground first. For example... in my old firebird I had my air horns and one of my fog lights grounded to the same point. Everything worked fine for a while, but once that ground began to corrode a tad, only one fog light would work with the switch. If I pushed the button for my air horns, the horns wouldn't work, but one of the fog lights would come on. Moving the grounds and making sure they were done properly eliminated the problem permanently.
So anyway... how do you secure a good ground? If it's inside the car, find a good thick piece of metal to drill into. Make sure you're not drilling into something important (like your gas tank). DO NOT drill anywhere into the hump behind the rear seat. Even if you don't drill all the way into the gas tank, having screws in that metal can puncture the gas tank in an accident and cause an explosion. Find a different spot. Anyway... the screw you use should be large enough to tightly hold down the washer and ring terminal. Your ground wire should always be terminated with a ring terminal:

The color of the plastic indicates the gauge wire that the terminal is designed for. Yellow is for 12-10AWG. Blue is for 16-14AWG and red is for 22-18AWG. Make sure you use the proper size. If you use one that's too big, it won't secure the wire properly. Crimp them securely with good crimpers.
After you drill your hole, you want to take a razor or screwdriver and scrape away the paint until you have bare metal in the spot where the ring terminal will touch the body. You want a clean, metal to metal contact point.
When you attach the ring terminal to the body of the vehicle, use a "star" washer (also known as a tooth washer) between the ring terminal and the body of the car:

The star washer will help dig into the metal and provide a better connection.
When you're grounding equipment outside the vehicle (such as fog lights) you want to follow the same procedures, plus add a few additional. Generally you can find an existing body bolt to ground to instead of drilling a new hole. Any crimped connections you make should included a dab of di-electric grease in the connector before you push the wire in. Heat shrink tubing should be used to make an air-tight seal between the connector and the wire itself. In cases where that's not possible, wrap it tightly with electrical tape. In many cases, soldering is an even better option than crimp connectors, although wires that are prone to high amounts of vibration are better off with the crimp connections and heat shrink tubing. You want to clean off the grounding spot just like mentioned above, but you want to make sure that you use di-electric grease on the ring terminal and star washer. If you don't, the connections will quickly rust and ruin the good ground. When choosing a pre-existing bolt to use as a ground, make sure it's one that's part of a good chassis point (radiator support bolts for example) or at least something that's an integral part of the unibody structure (like a fender bolt). You don't want to use bolts that are part of a metal bumper, because they are only attached to the rest of the body through a few bolts, and if those corrode, your whole bumper is no longer a good ground. Chosing a location that's free from salt & water spray will also keep your grounds good for a much longer period of time (which is another reason why the bumper is a bad choice).
Rule #3: Proper gauge wire
Make sure that the wire you're using is of sufficient size. If you use wire that's too small, the resistance goes up, and you also have a potential fire hazzard on your hands. For example, if you have a powerful stereo amp, and you use some tiny wire for the ground, the resistance will be high enough to induce a ground loop, just like if you had a bad ground. You can check your ground all day long, and it'll measure fine, but when you pass big current through it, it'll no longer be sufficient. Likewise, if the wire is really too small, it can get hot and melt. This can obviously be very bad.