Hey Tio.
To join two pieces of copper together, I just place them on the cooking burner of my stove. Electric or gas doesn't matter.
The metal they use to join them is solder. This usually comes on a spool and looks like a thick wire. It's soft and flexible though. You'll also need to buy flux. It's a cleaner used for soldering, and makes the solder flow down into a crack when it's liquified.
Coat both surfaces to be joined with flux.
Place the two pieces together on the stove, the way you want them when finished. Turn on the burner.
When the copper starts turning dark, it's hot enough. Feed the solder 'wire' into the joint. It will turn liquid as soon as it touches the hot copper, and run into the joint. Feed in plenty of solder to avoid leaks.
Turn off the stove, letting the copper sit and cool off. After 10 minutes, you can pick it up using pliers, a wire, or whatever metal tool is available. Hold it under cold running water for a bit, and it's done! Do not touch the copper while on the stove.
This can smell bad, but not for long...do not breath the smoke from the burning flux!!
You can use flux and solder made for water pipes, but silver solder is best for use on a waterblock, cause it transfers heat better. You can get silver solder at an electronics supply store, and use the same flux. I like the paste type flux made for water pipes because it's a little sticky and won't run out of the gap too much.
Use dish soap to clean up any flux left on the copper, and on your hands. It's a mild acid and will tarnish the copper over time, or burn your eyes badly.
As for the drill, see if an auto parts shop will rent tools out. Some here do.
Good luck.