I go to the sink and rinse out the bowl first, then once its clean I pull the trigger back while its still under the faucet until clear water runs out.
Then I take apart the nozzle cap and nozzle, wipe the needle and hold the nozzle under the faucet and then blow through it.
It really seems to me like paint gets stuck in the nozzle almost every time, I clean it every few colors and every time I'm going to do detail work. I don't use a needle to scrape paint from the nozzle also, because scratching the surface will just give the paint something to hold on to and it will clog worse. I use a toothpick carved to a point, being careful not to let it break off inside, and then I twist the corner of a paper towel with iso alcohol on it and push it through to get the rest.
Next I lube the end of the trigger, where it slips into the hole, lube the needle and put it all back together.
Seems to work good but kind of a pain.
I want to try auto air restorer. Heard nothing but good things about it. Ive used Createx airbrush cleaner and it is worthless, but the Iwata cleaner that came with my HP-CS worked really good. Seemed kinda soapy, I wish they gave me a bigger sample.