I learned that orchids cannot be planted in our clay soils, but instead require VERY well drained neutral soils. Roger suggested a way to get around this obvious snag for most of us by sinking a pot containing a well-drained substrate. The substrate Roger recommended is 2-parts granite grit; 6-parts perlite; 2-parts potting soil and a handful of oyster shell. Granite grit and oyster shell can be sourced anywhere chicken supplies are sold. With this method, the orchid will live its life in the sunken pot (using at least a 1-gallon pot), until it grows large enough to be divided. YouTube has a video on dividing terrestrial orchid clumps at https://www.youtube.com/watch?v=OS9ht0J8LDs, and it give a good view of what the rhizomes look like.
Where to sink the pot is also very important. Terrestrial orchids should receive no direct sunlight between 12:00 and 4:00 PM, but they also don't like dark places (full shade). I found a spot on the east side of the Jungle where the orchid will receive bright morning sun, but shade from trees the rest of the day. So far so good.
If lady slippers are in your future, be certain to procure your plants from reputable sources that ensure that their plants are nursery propagated and not collected from the wild. The Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES) has declared all members of the family Orchidaceae formally protected. There are strict controls on trade and import and export of all orchids. In addition, orchids have varying levels of rarity and protection throughout the United States, and laws vary from State to State. Some species are federally listed under the Endangered Species Act (ESA). If you are lucky enough to view an orchid in the wild, leave it be unmolested so that it can continue to reproduce and provide joy to the next traveler who happens upon it.
Several lady slipper species are native to Illinois, including Pink Lady Slipper/Moccasin flower (C. acaule), White Lady Slipper (C. candidum), Lessor Yellow Lady Slipper (C. parviflorum) and Showy Lady Slipper (C. reginae). With the exception of the Pink Lady Slipper (C. acaule) which requires a very acid soil environment, these Illinois natives prefer a neutral very well drained site similar to most hardy terrestrial orchids. With advances in terrestrial orchid propagation, all are available through specialty nurseries. In addition to straight species types, there are also a number of hybrids available.
I also noted in my research that Asian types require a dry winter. To achieve this in Illinois and much of the U.S., something impermeable like a sheet of plywood would need to be placed over the plant during the winter months to shed away any snow or rain.