I use either white spirit or humbrol enamel thinner if I have been using enamels. If its acrylics I first flush through with water and then use a specific (in my case Vallejo) airbrush cleaner. The reason for this is that it also contains a lubricant of sorts that keeps the micro 'o' ring from perishing or degrading.
My process....
Empty paint from the cup, wipe it out with toilet tissue, its finer than kitchen roll, you could also use normal soft tissue for noses, but toilet tissue is cheaper.
Operate airbrush into an empty jamjar, make a cup shape over the top with your spare hand and insert the airbrush between thumb and forefinger, this keeps paint in the jar. Once excess paint has been removed, I then put cleaner (either white spirit, water for whatever medium I have been used) and repeat this process, after 10-20 seconds remove from cup and cover the spray nozzle with a finger or paper, be careful of needle point! Pull trigger to back flush air into the cup, this removes any residual paint. Repeat the jamjar process. Empty any residual from the cup into the jar.
Put fresh cleaner into cup and give a 10 second burst into the jar, what is left in the cup empty on to soft cloth or wad of tissue and wipe over the outside of the brush.
It sounds like a long process, but takes about 90 seconds in total.
Finally I have 3 brushes, one I keep for acyrlics, one for enamels and one for priming. The primer and enamel brushes have 0.3mm needles and tips, the acrylic a 0.2mm tip and needle. Some people will say don't use enamels as the solvents damage the brush, this might be true, but I've never encountered it
Finally, once a week or so I strip the airbrush down into its component parts for a thorough clean - again some people go overboard and use one of those high frequency jewellery cleaners, I don't because I haven't got one
but checking the needle for dried spots and the tip and its cover is good enough.
Finally can I give a shout out to
www.everythingairbrush.com this company has always given me good service and only 2 weeks ago supplied me with free stuff! I had sent them an email asking if they did a replacement needle and tip for my enamel brush, I had carelessly knocked it off the bench during a strip clean, It landed on the blunt end of the needle and punched the pointy end through the tip damaging them both beyond repair. They no longer stocked my make of airbrush but searched out their storeroom, found some old stock and sent me a brand new needle and tip set free of charge, you can't get better service than that.