The hard way to get started with Luna moths (or the other native silk moths), is to go out into the woods with about 1000 watts of lights and a bed sheet. Hang the sheet near the lights. The lights do attract moths and if you’re really lucky a female might land on your illuminated bed sheet. The females don’t fly until they’re mated and hence if one lands on your sheet and you catch it, you should be able to collect some eggs to start with. Put a mated female moth in a paper grocery bag and she will lay lots of eggs. Those will hatch into very small caterpillars in about 2 weeks. I have not used the lights method myself; too much work.
The next hardest approach is to collect cocoons from trees in the spring; before the trees leaf out. I have done this, and it works pretty well to get started with Cecropia, polyphemus, or Prometheus moths. When those moths (caterpillars) spin a cocoon, they usually also attach a little silk to a tree branch. This holds the cocoon to the tree after the leaves fall. Just look for oblong debris hanging from a tree in the spring and it might be a cocoon. Pick them off the tree and put them in a cage. The moths will start emerging in late spring after the trees have leafed out. Unfortunately the Luna’s usually form cocoons by wrapping themselves around a leaf or two, and when the leaves fall, so do they. They then get mowed over or burned in leaf piles! That makes them harder to find. Unfortunately a lot (30%+) of the cocoons you find in the wild will be parasized (eaten alive over winter) by parasitic wasps and flies. If the cocoon feels ‘light’ it will probably be a dud.
Another approach I’ve successfully used is to carefully observe the moths favorite host plants in mid summer. If you see an area with a bunch of damaged leaves, then SOMETHING is eating at it. Sometimes you will get lucky and find a giant caterpillar.
The easiest way to get started with moths is finding a local bug guy who happens to sell eggs at garden events, or buy eggs from a source on the Internet. I have purchased from a couple of sources over the years, more recently from a guy in Canada. He’s also got a good website with more details how to raise the various silk moths.
Here’s a link to his page about Luna moths; how to raise, etc.http://www.silkmoths.bizland.com/Actiaslunarearing.htm
Like with honeybees, there is a learning curve with moths. You should expect plenty of failures along the way. Personally I find the Polyphemus are the easiest moth to raise. The Luna’s are a little more fragile. I find the Cercopias (aka Robin moth) the hardest to raise.