Great ideas from all above. If you're certain the business end of the AB is clean and in good physical condition, then my suggestion is to get a supply of thinners and paint, then as was said get plenty of plastic to paint on, then experiment with different thinning ratios and pressures, plus distance between the AB and surface to be painted.
When spray painting, one of the most critical elements is lighting. A poorly lit space for spraying is an invitation for unwanted results.
The old saying about beginning with airbrush painting is to practice, practice and then practice some more. My first attempts at airbrushing, using an AB similar to your H were terribly disappointing, and I was not seeing any improvements as I continued. I seriously thought I was just not able and was resigned to brush painting.
My stubborn Irish side said "just get with it." So I get a bunch of plastic sheets and large jugs, then spent most of an afternoon spraying out several bottles of model paints. In time I saw what worked well, and even more important what didn't work.
Cleaning of the airbrush after use is one of the most critical parts of spray painting, I know many folks consider a rinse spray to be good enough, in my experience it just isn't sufficient. When you're through it's easy enough to remove the front parts and the bottle feed tube to the AB, then give them a thorough cleaning and reassemble. Just a very few bits of dried paint left inside the parts, will have a disastrous effect on future spray jobs.
Also, as you spray, keep an eye on the sharp pointed needle end, a q-tip and some thinner will clean any drying material there with just a quick swipe. If the paint does dry there it will cause spitting of little droplets and spots getting on the surface you're painting.
Last, if you haven't yet by all means have a look at "Don's Airbrush" site, listed as that on Google. There is info on your H, plus all other things related to airbrushing. Very well worth the time.
Let us know how you make out, if you have the time.
Patrick