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| How do I implement the third wire (earth) on a power supply? |
It might help to think of the three wires as hot, electrical ground, and safety ground. Electrical ground and safety ground are connected at one point in your house (probably back at the breaker box) so theoretically they're equal, but due to differences in resistances between the two at any outlet, there's usually a small voltage drop between them. Therefore, if you hook anything up to safety ground, you're likely to get a ground loop with anything that you attach that uses electrical ground instead.
The primary purpose of safety ground is to connect to the chassis of equipment. That way, if you get a short to the chassis, the current has somewhere to go: to ground. This will usually trip a breaker or blow a fuse. That's why it's called safety ground. If the chassis were left floating, the chassis would stay energized until some poor guy came along and touched it, providing a path to ground through his body!
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| Do I just use the Negitive as a ground and not connect the "grounds" to the earth? |
Study some schematics for power supplies. You'll see that the electrical ground and hot potentials go through the transformer. The only things you connect directly to these wires are the transformer, usually fuses, and sometimes AC-side filters. The power supply proper is on the transformer's secondary side, as is whatever you are powering with this power supply.
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| How do I calculate for the DC end? |
There are no calculations, only rules of thumb. They usually go something like, "multiply your operating current by 2". The reason is, you have to account for the inrush current of the power supply.
Personally, I just try different fuses, going lower and lower until I start blowing them, then I go back up the scale a little bit. Fuses are cheap; get a bunch of many different values.
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| where do I put that fuse? |
Between the transformer and the bridge is a popular place. This protects against faults inside the power supply, downstream from the transformer; a shorted filter cap, for instance. You sometimes also see it on the output of the supply, where it protects against faults outside the power supply.
