Thomas Mayer
I clean my airbrushes using Revell´s Airbrush Cleaner. In case of very resistant clogging (absolutely very rare) some Nitrocellulose thinner helps. But in about 99% Revell´s stuff does the job.

Kevin Ekstrom
You can buy a good airbrush cleaning set on eBay for under 5.00 USD. I wouldn't waste extra money for a name brand cleaning set. You're only paying the extra for the branded name.

Ebay.com Item - 11PCS Stainless steel Needle Brush Set Airbrush Spray Cleaning Repair Tools Kit