There's hundreds of welding Instructables around, many of them quite good. I'm writing this one here to share a technique I've developed that works quite well, even on copper tabs (for which it was designed).
The theory is simple- I've got a handful of ultra-capacitors (2.5 Volts, 2600 Farads) wired in series, then discharged through the material. The devil is, as always, in the details.
Anyone who's tried will tell you copper is a pain to weld- for many of the same reasons you probably *want* to be using it in your project. It's got about five times the thermal conductivity of iron, which basically means you need to pump in a lot more heat to overcome heatsinking. When it comes to resistance welding (which is how spot welding works, unlike other electric welders, which use arcs), you've got even more pain coming- the conductivity is another 5 or 6 times higher. So your welder needs to output 5 times more current just to create the same amount of heat.
Put all this together, and it means you probably need a welder that's over 20 times more powerful than a typical steel spot welder.
Step 1: Bill of Materials
I'll hardly claim that I've got the best setup here- but it does work, so this is probably a good place to start. To replicate my setup, you'll need:
* 4 ultra capacitors.
-I used Maxwell "Boostcap"'s, rated for 2.5V at 2600F. I believe mine are surplus from electric buses regenerative braking systems. I got mine for about $10 each from the Electronics Goldmine (http://www.goldmine-elec.com/), but it seems they're sold out at the moment. You can find them on eBay, too. Make sure they're rated to have low series resistance (in other words, they should be able to provide a lot of current- mine should do 600 amps).
* 3 lengths of heavy gauge wire, with suitable ring terminals on each end. I used scrap I had around- I think it's about 6 gauge, roughly 2 feet long. Each is a different color in my setup.
* thick copper tubing, about 3/8" ID, 1/2" OD. You need two pieces, each about 3 inches long.
* a graphite block(s), enough to yield two pieces about 0.5"x0.5"x3.0"
* two big hunks of copper. I used a 1/2" plate roughly 5"x5", and a cube about 3" to a side. It's not critical.
* Some sort of DC power supply- I used a standard benchtop variable DC supply. It's limited to 3 amps, so charging takes a long time. You could do much better.
* Some means of clamping your electrodes: I used some G-10 fiberglass stock (not the best choice, but fairly temperature resistant and non-conductive), with holes drilled for the electrodes, and a rudimentary hinge. Again, you could do better than my quick-and-dirty solution.