First off, check all of your gear for functionality before you head to the playa. There's nothing worse than bringing gear out to Burning Man that is not functioning. A simple test run before you pack should save you a world of hurt when you arrive to Black Rock City.
Cables and Adapters
Have a variety of cables and/or adapters for any situation. If an amplifier were to go down, would the current amplifier be able to handle “daisy-chaining” your speakers, and do you have the right cables to connect them, including XLR to ¼, XLR to RCA, ¼ to RCA, Speakon to Banana, or any possible connection that you would need? When you can, bring backup gear, just in case something goes down, including backup mixers, amps, monitors, extra cables, etc. During the 2010 Burning Man, Bassnectar’s audio interface would not work and he was not able to play at Root Society because he didn't have a backup with him.
When leaving camp consider covering the equipment before you head out, even if it is just a garbage bag over the speakers. If you suspect that a sand storm is coming, consider moving what equipment you can into cars for better protection. Flight cases, Decksavers and covers for the gear are perfect to minimize the amount of playa dust that gets into the gear.
Dust of any kind is the enemy of all electronics. It acts as a thermal insulator, and causes the gear covered in it to operate at a higher temperature. Once the temperature exceeds whatever the component/chip/resistor/etc can handle, it stops working. Playa dust is especially harmful not only because the particles are so fine, but because the alkali content acts as a mildly corrosive agent. Compressed air or canned air can help clean out the gear while on the playa. If you really want to be dust-free, think positive pressure ventilation and HEPA filtration.
Keep the equipment at cool as you can. Place your equipment in shaded areas to prevent overheating and causing damage to the equipment. Part of that is keeping the equipment off of the playa itself, as the playa retains and transfers lots of heat. If you are using stands, make sure that they are well secured. The winds/sand storms can easily knock over equipment.
Lighting for Burning Man
LED lighting is the way to go on the playa. It uses significantly less power, creates less heat and there's practically no maintenance involved. Par cans and uplighting are the most common effect lights used to light up camps at night.
Amended: Battery-Powered LED Lighting
LED lighting's low use of power allows for a bit of saving grace with so little access to electricity. Battery-powered LED lighting has come a long way, with some lighting lasting up to 20 hours on a single charge.
Power GeneratorsGenerators are necessary for amplified sound and lighting on the playa, they are beneficial to you, but can impact those camped around you. Taken from the BurningMan.com website: “The hum of generators can become annoying over a long period of time. Please keep your neighbors in mind. We recommend generators that are sound insulated. DO NOT dig a trench to sound-insulate your generator. Rather, enclose it in a wooden box.”
Power conditioners are key to protecting your equipment more than in the default world. Power from generators is inconsistent (at best) and could cause some serious problems if you equipment is not protected.
Returning from Burning Man
When returning from the playa, take the time to clean out the gear and wipe down with a water and white vinegar solution. Some equipment will have to be wiped down a few times to take off the playa dust.
BurningMan.com website regarding sound in camps: “As a community, we need to work together to keep sound at desirable levels. This means that everyone involved is personally responsible for how they affect everyone else's experience. If your neighbor believes your sound is too loud, you must work with them to find an acceptable volume. You will need to check in with those that you are camped near to find out what other events are planned and work with them to create a schedule. With these actions you should be able to handle all of your own sound issues. If everyone works together there will be no need for Black Rock Rangers to monitor sound. Please pass this information around to other participants in your theme camp or village and to those that are not planning on being listed on the map. A community effort is need to pull this off.”
NOTE: In almost all cases, playa dust will void your warranty of new products (it's often considered abuse or neglect). Taking the time to protect your investments can give them years of happy life.