This method is more time-consuming than others, unless the LEGO only has minor dust and dirt. Use this for your favorite or most collectible LEGO, to keep them safe from accidental damage. Set aside any pieces with stickers or printed patterns, as well as any multi-part units that are not meant to be separated, such as turntables. Scrub these with a dry towel, or remove serious grime using a new toothbrush. Delicate electrical parts can be cleaned using alcohol wipes instead. Detach all non-water-sensitive parts from each other, unless they are stuck. Make sure to pull apart multi-piece units such as tires. If you have a large collection, divide them into containers of about 200 or 300 each. Place the separated LEGO bricks in a container. Add lukewarm water and a little dish soap or other mild detergent. Agitate the bricks gently, stirring them around with your hand.  Never use a cleaning product that contains bleach. Never use water above 104ºF (40ºC). If the bricks smell bad or if you would like to sanitize them, add white vinegar to the water. Use approximately ¼ to ½ as much vinegar as you did water. Leave them to soak for at least ten minutes, then check up on them. If the water is extremely murky, replace it with fresh soapy water and leave to soak for a full hour, or overnight if convenient. If there is still stuck-on grime, you may need to scrub it off using a new toothbrush, or a toothpick to reach crevices. Clear plastic pieces such as windshields are easily scratched. Rub them with your finger instead. Transfer the LEGO bricks to a strainer or colander and rinse them in cold water to remove the soap and loosened grime. Optionally, spin the bricks in a salad spinner to remove some of the water. Next, place the wet bricks in a single layer on a towel, right-side up so water drains from the underside. To speed up the drying process, leave a fan on blowing over the bricks. Do not use a hair dryer, which can damage the bricks.

Summary:
Use this method to minimize damage. Scrub water-sensitive parts with a dry towel or toothbrush. Separate all remaining pieces. Agitate in soapy water. Add vinegar (optional). Let the pieces soak. Scrub the pieces if necessary. Rinse the pieces. Dry the bricks.