What kind of airbrush is it? In general, to clean it, just run some thinner through it after using it and that will take care of it. Some are finicky, some are pretty forgiving. Best thing I can recommend is to use the manufacturer's recommendations.
As a very rough rule of thumb, paint should be thinned to about the consistency of milk. That is going to vary depending on the airbrush and the pressure. I spray Tamiya and Model Master acrylics mostly, and thin them about 3 parts paint to one part thinner. For thinner I usually use 91% isopropyl alcohol, but that will cause Tamiya paint to give a flat finish. If I need a gloss finish I use Tamiya thinner with Tamiya paints. I Also usually add a couple of drops of acrylic retarder to the mix to slow down the drying time. I spray at about 15 psi pressure, and about 4" to 6" from the model.
These are going to vary for you, because everyone likes to paint a little different. Just play with your airbrush on a scrap model and find a combination that works for you. You aren't going to ruin your brush, it's designed to have paint blown through it, so just have at it. If you have any problems there is usually someone around here who can help.