First, go to a Paint Retailer (found in the Yellow Pages under PAINT - RETAIL), and buy some good paint. Bring in a sample of the siding in case they have any questions (if possible). A broken piece will do just fine. Spend some GOOD $$$ on some GOOD paint. Don't skimp because if you do, I guarantee you'll be at this job again in 5 years! You want a paint that is of a 'rubbery' consistancy. (I forget what it is. This type of paint kinda 'holds' the shingles to each other. Maybe someone else knows what it's called. The retailer should know.) It will cost you but it's better than doing the job again in 5 years. Get the right brushes too while you're there. Read the can carefully. You shouldn't have to prime unless they're new shingles (I think. Ask the retailer.) Read the instructions on the can carefully. The prep work is the key.
Then, buy a mask that's rated for asbestos fibers. The major Home Centers sell them. (I bought mine there.) Then, remove the loose paint. Replace/repair damaged shingles. Power-wash the walls under light pressure. (IMO, the traditional garden hose doesn't supply enough pressure.) Don't leave the water stream lingering at one spot too long. Depending on how the shingles are attached, especially with water under pressure, it's easy to get water behind the shingles. Just make quick passes and only a few. You're mainly looking to knock off the surface dirt. Let the house dry out a day or 2 (so time your job to the weather, and only wash off a side at a time, or as much as you can paint in your alloted time.)
Other than that, wait for others to post-up with info. My best to ya and hope this helps.