To plug in a wall, all you would need is a bridge rectifier (4 diodes, and a small filter capacitor) to change 120VAC to 120VDC. Hell, you could run them off AC, but there would be a small flicker. to hook up 12, I would run all 12 in series. Assuming each LED will draw 20mA, and has a 3v drop (I use that for all of my LED calculations, and I do do a lot of them), you're looking at a string with a 36v drop, and 20mA current draw. plugging in (120-36)/0.02 = 4.2k ohm current limiting resistor.
For batteries, the smallest would be a 3V watch battery. Most LEDs will run off 3v drectly without the need for a curent limiting resistor. Off of a 3V battery, you would have to run all 12 in parallel, giving you a 240mA current draw. The battery wouldn't last very long. 2 AA batteries would also work. With a 240mA draw, a typical set of AA batteries should give you 5-6 hours of battery life. I once built a flashlight using 19 white LEDs. It ran off of 4 AA batteries. All of the LEDs were run in parallel with each other (Why I didn't just do a series-parallel configuration I don't know, it would have been more efficient.). Anyways, I built it years ago, and have taken it camping many times. I've never changed the batteries.
