Spray the white plastic deck chairs with a garden hose. This should remove an initial layer of dirt, cobwebs and debris.
Fill a bucket up with hot water and dish soap. Use a sponge to wipe the chairs down. Rinse off with the hose.
Fill a spray bottle up with a 2:1 ratio of water to vinegar. You can purchase a cheap spray bottle or rinse and reuse the spray bottle of household cleaning solutions. You needn't use more than a cup of vinegar. Spray the entire chair with the vinegar solution, and allow it to sit for a little while. Use a sponge to scrub the chairs. Rinse off with the hose. Dry with a towel.
Spray the entire chair with the bleach cleaning solutions. Allow the solution to sit for a little while. Use a sponge, and scrub the chairs clean. Rinse off with a hose and dry with a towel. Repeat this step as needed.