Step 3: Get an Amplifier and Battery (and Charger)
You will need an Amplifier. The amp discussed here is a standard ordinary car audio amplifier (except the switch we added). Amps like this have one input - a "Line-Level" stereo input. This signal can come from an IPod or other headphones-ready device, OR a mixing board with several inputs (including Microphone jacks). Amplifier wattage numbers are very subjective, so don't worry about whether it says it's 200 watts or 1000 watts, just see if it WORKS and sounds good. It will probably supply more wattage than your speakers can handle either way though, so be careful.
(When testing a suspicious used amplifier, don't connect it to a speaker you don't want to fry!)
Another thing about a Car Amplifier like this: it runs on 12 volts, like a Car Battery supplies. Using your home stereo amplifier won't work unless you have a very long extension cord. You may be thinking "but I can just use an inverter, and power my favorite plug-in amplifier!". DON'T DO THAT. You will be wasting a third of your battery life, carting around extra equipment, AND inverters make a horrible 120Hz "buzz" that gets into all your sound. Plus people who know better will scoff at your lack of efficiency.
You will need a Car Battery to power your soundsystem. It can be a used one, a small one, a largish one, or a Boat battery, or other 12 volt battery of a decent size. Deep Cycle batteries are better, but more expensive - basically, they can be drained further without lasting damage. Ordinary car batteries are not supposed to be drained more than halfway during normal use. But if a Car battery is available to you, use it. You probably won't drain it more than halfway anyway before the Cops take it away. (Try to get them to let you disconnect the battery so it's still good when you get it back!)
And the Charger: batteries like this must be charged back up after being used - allowing them to sit discharged will ruin them, besides not being ready next time you want to party. I recommend strapping the charger into the shopping cart and wiring it in - so there is no reason not to plug it in when you get the chance, even if the cart doesn't go "home" to the same place every time. You can't skip this step; charging is essential to the preservation of your battery and your whole project.
Read up on car battery chargers to understand how long to leave it plugged in, and what Charge Rate to set your charger to. If you have an automatic charger with a two-amp setting, overnight will charge your battery back to full, and you can leave it plugged in up to a day or two without danger.