When changing colours while spraying, it's usually sufficient to run a bit of thinner (suitable to the paint that you're using) through the airbrush between colours. Exceptions to this would be while weathering, where there should be no need for this step, and when making drastic colour changes, like from black to white or yellow. In the latter case, I prefer to do a thorough cleaning, although if you plan your colour application sequence properly, this shouldn't occur too often. If you've been painting, then want to apply a clear coat, I recommend a thorough cleaning, as outline below.
When you're done painting for the day, it's easiest to clean the airbrush immediately. I usually use lacquer-based paints, so I first run a cup of lacquer thinner through the airbrush. I then remove the cup, refill it with lacquer thinner,and place it in the spray booth. Next, disassemble the airbrush. The aircap, aircap body, and tip go into the lacquer-filled cup. Set aside the handle, locknut, and adjusting sleeve and spring. I keep two cans of lacquer thinner handy, both labelled as to their purpose: one is for thinner, and this is used for nothing else, so it cannot be contaminated. The other is labelled "cleaner". Wipe the needle with a rag, then dip it into the cleaner, then wipe it dry. Remove the needle support assembly from the body shell of the airbrush, and run a pipe cleaner (which has had one end dipped in thinner) through it, wet end first, from the rearmost end. This will clean and dry in one pass. Wipe the rocker end of the assembly with a bit of thinner on a rag, dry if necessary, and set aside. Using the same pipe cleaner, re-wetted if needs be, insert it into the rear of the shell, feeding it through the opening for the needle, and draw it out through the front end. Now, feed the pipe cleaner into the fitting where the colour cup attaches, allowing it to curve inside the body shell and exit from the business end of the airbrush. Using the reamer, or other appropriate tool, fish the small parts out of the lacquer-filled colour cup, one-at-a-time, drying each with a clean rag. Gently insert a clean, dry pipe cleaner into the back of the tip to dry it. (don't force it in, as the wire in the pipe cleaner can distort the opening - you're just removing excess thinner, so a quick, light touch will suffice). Dump the thinner from the cup either back into the can of "cleaner", or, as I do, into a bottle of plastic cement. I use lacquer thinner when cleaning the airbrush after spraying acrylic paints too, as I find that soapy water is not as effective and creates more of a mess. Dry the empty colour cup, using a clean rag or pipe cleaner, as appropriate, then re-assemble your airbrush. The entire task takes less time than it takes to describe the procedure.
Wayne