To make the power supplies I just soldered some wire onto the ends of the batteries I had bought so that I could easily attach the LEDs to them. The 9V battery served as my 9V power supply, one AA battery made a 1.5V power supply and three AA batteries bundled together made a 4.5V (1.5V + 1.5V + 1.5V = 4.5V) power supply. I didn't use alligator clips on the ends of the wire, but they would have been helpful here.
I think they have a thing called lilypad for clothing and you can use thread thats conductive look at sparkfun.com they have it also you would probably want to use smaller leds maybe SMD.
What about using one of those wall plug things that come with so many electric things? They usually have the voltage and amps stamped on them someplace.
I fly electric model airplanes and have soldered up many battery packs. The secret is to tin the battery terminal first then solder the wire to it. You should use at the very least a 30 watt iron to get the heat to the terminal as quick as possible so that you don't heat the battery too much. It is important not to get the battery hot as this may ruin the battery and could even lead to thermal runaway and possibly an explosion.
Solder anything to a piece of aluminium?!? If you know how to do that, please tell me!
In normal atmosphere, aluminium coats itself with a (very thin) layer of aluminium oxide. Which can't be soldered with anything I know about. It might be possible in a nitrogen atmosphere with very powerful (reducing) flux.
With aluminium, IMHO crimping is the way to go. But with LEDs I would just use the good old copper wires.
Aluminum can be soldered with products made for that purpose; not practical to buy a $20+ pack of AL rods unless you're going to do a lot of work with the material.
Never solder anything to a battery. Instead, use a battery pack and place the batteries into that. Soldering to a battery can/will make it explode, and battery acid will get everywhere.
Lookup the MSDS for Energizer alkaline batteries which recommends not soldering anything to the battery because the solder can cover the vent holes which keep them from exploding in the event of extreme heat or general failure. Ever leave a battery in a device for a long time and come back to find it corroded, yet no evidence that the battery exploded? That's because the catalyst can ooze through the vent holes rather than building up pressure. "Batteries normally evolve hydrogen which, when combined with oxygen from the air, can produce a combustible or explosive mixture unless vented. If such a mixture is present, short circuits, high temperature, or static sparks can cause an ignition." http://www.officedepot.com/pdf/msds/696526.pdf
You can also try an AC to DC power supply such as a wall mount transformer or house plug. Be sure to use a voltage regulated power supply or the voltage will be higher than required if your circuit does not draw the specified current. This page has lots more info on basic LED circuits: http://www.lunaraccents.com/nav-educational-LED-information.html
If your going to use the battery just temporarily to play around with electrical tape will work fine. If your building something thats going to be more a permanent installation I would recommend getting a battery holder. You can then solder your wires onto the holder directly and change the battery as necessary.
And you can use any kind of batteries
In normal atmosphere, aluminium coats itself with a (very thin) layer of aluminium oxide. Which can't be soldered with anything I know about. It might be possible in a nitrogen atmosphere with very powerful (reducing) flux.
With aluminium, IMHO crimping is the way to go. But with LEDs I would just use the good old copper wires.
I have soldered directly to both dry, and wet cell batteries and have never had an explosion issue. Then again I *do* know how to solder!