Ventilate the workspace to avoid hazardous fumes from the paint and chemical solvents. An electric fan helps with circulation as well.
Use a scraper to chip and peel any of the old paint that has already started to come loose from the wall. Removing as much of it as possible before resorting to a solvent will save time.
Select a paint thinner in an application that is appropriate for the task at hand; household solvents such as acetone and rubbing alcohol might normally be an option, but old paint that has fully cured is beyond this point. Liquid and aerosol thinners are most efficient for removing one to two layers of old paint at a time.
Protect your hands from alkaline burns with a pair of rubber gloves. Apply the paint thinner with a dry rag or spray can according to the directions on the product label, then allow the old paint to soften for the instructed period of time.
Lift the paint gently with the scraper blade and follow up with a scouring pad or high grade steel wool to scrub the remainder. Rinse the excess paint and chemicals from the wall using a wet sponge or cloth.