I have tried to write this article with the aircooled VW in mind, but as I have not written anything too specific to the VW you could apply it any car.

Let's start with a look at the way the electrics work on your car. You have a battery to store the current, a generator to replenish it and an ignition switch to provide power to a majority of the car only when you are there or when the engine is running.
When the ignition is off there are some areas of the car that still require the power of the battery, namely the interior lights, the parking lights and the radio memory or in some cases the whole radio. That is only a short list, but there really isn't too much else on a non computer controller car that requires any power.
When you switch on the ignition you then begin to power many more parts of the car even without you intentionally switching them on. For instance the lights that come on on the dash display, those are the oil and generator warning lights, the oil light is switched on when the engine oil pressure drops below about 6psi (1/2 bar) and obviously when the engine isn't running it will light up as the pressure is 0 psi. This enables us to use this as a bulb test. If the light doesn't come on then the bulb doesn't work or there may be another problem, but we'll stick with the basics at this point. Also the generator light comes on, this is a voltage comparison between the battery and the generator output, so if the fan belt breaks the voltage output of the generator will be less than the battery and the light will come on and with the engine not running the light is obviously going to light. If this doesn't happen, then you may have either a bulb blown or another fault.
If either if these lights fail to light with the ignition then look into it now not later. Imagine the bulb for the oil pressure warning had blown and you drove off without changing it and whilst on the road your sump nut came loose and all the oil poured out your engine would seize up and the first thing you would know about it was a loud bang.

A common statement I have heard over the years is "The car won't start the battery must be flat" when in fact it's a problem with the engine not the battery. If the starter motor turns the engine over then the battery is working fine. If the engine will not turn over at all, turn something else on, a radio or the winscreen wipers and if they work then the battery is not the fault. Trying simple tests like this could save you looking a fool in front of the recovery guy and maybe any call out charge.

If you decide to recharge the battery, remember to do out of the car and not in. When you remove the battery disconnect the negative lead first (this is probably bare woven wire), so if you touch the bodywork whilst loosening the nut (remember you don't need to remove the nut) it won't matter, but if you still have the negative connected whilst trying to remove the positive and you touch the body you can weld you spanner to the battery, that's frightening, I've done it.

There are things to look out for when the engine won't start, does the starter motor click? Turn on the ignition, this can make a small clicking noise as the relays turn themselves on, but when you turn the key to the starter position is there any noise? If there is a click, that is the solenoid that provides the starter with the power to turn the engine over, if it doesn't then you have no power to the solenoid which comes straight from the ignition switch.
On a Beetle there is a connection under the back seat on the opposite side to the battery, check that this is connected, it should be red/black.
The coil is the tin can shaped thing with the thick black cable coming out of the middle and going down to the distributor. It should have a minimum of two wires attached to it, one to the positive side (15) and one to the negative side (1). The negative connection should come from the distributor and is probably green whereas the positive lead on an aircooled VW is usually black. Also on the positive side there is likely to be a wire going to the carburettor to power the shut off valve and the choke. To test these and any electric supply leads is with a bulb with two wires soldered on, I use an indicator bulb. It doesn't matter which way the bulb is connected to the electric supply as the work both ways.

Wire has a set amperage, that is the maximum power that can be drawn down it. For example you could not power your headlights with the same wire you would use to feed your speakers. Wire is measured in strands and strand thickness which gives a nominal current draw. Here is am example, a roll of 14/0.30mm wire is 8.75amps, that means it has 14 strands of 0.30mm wire. The more strands you have the more current can be passed down it. Any wire must be fused between the supply (this is the battery) and the load (this is the object taking the power) and must be greater than the wires rating. You can calculate the required fuse with this formula: Wattage / Voltage = Amperage. This is best shown with spot lights, they are usually 55watts and the battery is 13.2 with the engine running, so divide 55 by 13.2 and you get 4.2, so an 8 amp fuse would be suitable for this lamp. Just remember each item on a line must be added together, so if you have 2 spot lights on the same feed you will need to double your figures, giving a maximum draw of 8.4 amps and therefore a bigger fuse and thicker wire.
If you have a fuse that keeps blowing and you don't know what is causing it, the only way to find out what it is is to switch everything off then slowly turn everything on one item at a time until the fuse blows again. Remember that it may not be single item that is causing the fuse to blow, it could be too much draw through one fuse and therefore when you have exceeded that the fuse blows.

Turn signal indicators flag because a sprung plate is lifted and dropped in a housing which makes then breaks contact at either end of its travel. They are designed to cope with a certain amount of current, usually 42 watts (2 bulbs) so if one bulb blows at some time the other one will flash twice as quickly. This is a good indication that one of your bulbs has blown.

A relay is a unit that allows a low power switch to turn on something that requires a much higher draw. A good example of this is a cheap plastic switch that comes with a set of spot lights. Without a relay the switch would burn out. As I mentioned before two 55 watt bulbs draw 8.4 amps and most plastic toggle switches can only cope with about 2 amps, so you fit a relay. The relay is only an electro magnet which when turned on makes a separate contact. This means that the low power circuit has no electrical contact with the high power circuit. A relay usually draws less than 1 amp so almost any switch will cope with this, and most relays can cope with about 30 amps.