I first got interested in making my own portable sound system for Burning Man in 2007. I wanted to make a loud and good-sounding iPod amplifier for our camp that ran efficiently from a 12V battery that could be charged with solar power.
I was vaguely aware that there were such things as Class D amplifiers, which don't waste any power heating up the transistors. They use the same technique used in switching power supplies, those tiny wall-warts that make as much DC power as a much larger transformer but don't get hot.
I looked around on the Internet and found that Texas Instruments makes a broad family of Class D amplifiers, and they even had evaluation boards available for fifty dollars. This is important, since the chips are teeny tiny and impossible to use without a custom printed circuit board.
I obtained an evaluation board for the TPA3107D2 chip, which is rated to drive two 8-ohm speakers at 10 watts from a 12V battery. I brought this to Burning Man to drive a large pair of JBL component speakers, and it worked just great.