Here are the basics:
Family Orchidaceae is a huge, young plant family. By young, I mean 'genetically in transition'. There's a whole lot of variation in the family, and the speciation has not become genetically ensconced enough to prevent wide-ranging interbreeding, once climatic, behavioral, physical, etc. barriers are removed (e.g., by keeping them in cultivation and hand-pollenating).
One of the adaptations of the family, generally speaking, is the development of very small seeds with no internal food stores. This means they can produce a huge number of seeds, which can be carried by the wind across long distances (e.g., across the Atlantic). It also means that their growth from seed is dependent upon finding beneficial mycorrhiza. These fungi convert available plant matter (dead leaves, compost, etc) in the ground or on the branch into a form available to the orchid seedling. If it is able to find compatable mycorrhiza, the seed germinates, forming protocorms, which then produce little tiny pseudobulbs and leaves, and then the orchid can take care of itself. In place of these mycorrhiza, we humans use a sugar/nutrient solution, which is usually made into a gel with agar in order to provide support for the plantlets. Since this is also an ideal way to grow mold and fungus and things of that nature, the seeds need to be sown and germinated under sterile conditions.
So, these are the two main things about orchid breeding: (1) you can breed a whole lot of quite different stuff together, and (2) you need a lab to germinate the seed.
Most people send their seed off to a lab to have them flask it. A number of places do this for a reasonable fee; Troy Meyers' is especially good if you're just doing species outcrossing (i.e., crossing two clones of the same species), but they're more expensive for hybrids. If you'd like to try "going commando" and setting up your own mini-in-home-lab, you can find (comparatively) easy to understand instructions and more information than you'll know what to do with at Aaron Hicks' Orchid Seedbank Project.
And, of course, this forum is a good option for asking questions. Good Luck!