Many Reiki practitioners use crystals and stones in their Reiki practice, either for their own use or healing (placing them under their tables or setting up crystal grids under them, or just laying around in the office, or on their person), or for their clients healing as in Crystal Chakra Balancing. However, incorporating crystals and stones into Reiki is not a part of Reiki. Dr. Usui, Dr. Hayashi and Mrs. Takata (to my knowledge) did not do this. It is a "New Age" thing and what I like to call and "add on" to Reiki.
Whether it came about as practitioners of Crystal Healing or other alternative healing modalities that used crystals in their practices already began experimenting with the combination or some other way/s, I don't know for sure but suspect that is how it happened. Those already experienced in Crystal Healing probably just added it in to their Reiki practice and found that it worked and it worked very well.
If you consider that most crystals and possible most stones contain some amount of water and that water is an excellent conductor of energy, then it's a "no brainer. " Apparently it's common for quartz crystals to contain varying quantities of water that (becomes) trapped within the crystalline structure, most commonly as water vapor which gives quartz its misty hue, or in other cases as in Enhydro, an actual pocket of water is encased within the crystal. In the case of the Enhydro formation, sometimes a small amount of air also ends up in the same space occupied by the water and as a result you have these wonderful specimens of quartz with bubbles inside them" (says one very adapt crystal lover).
Using Crystals/Stones with Reiki is quite the rage, well in my area at least it is. There is even a book out titled "Reiki with Gemstones" by Ursula Klinter-Omenka Many Reiki Practitioners become Crystal Healers (like myself) so that they can speak intelligently about them and have a good working knowledge about which ones do what and what to do with them. The world of crystals and stones is just a big as the world of Reiki - so much to know and so little time.
I tell my clients and students that the Reiki energy is enhancing what the crystals are doing when we place them on our clients bodies or our own , and the crystals/stones are enhancing what the Reiki energy is doing during a session. Most definitely a very powerful combination!
We typically see crystals/stones placed on the body during Reiki in several ways: l) Being placed on each of the seven chakras in the corresponding colors of the chakras for the purpose of bringing the chakras into balance. 2 ) We may receive guidance from "our team" (the Reiki Spirit Guides, Angels, and other Divine beings who are working with us at any given moment when we channel Reiki) to place a certain crystal or stone here or there on our clients body, or that they need to be working with a particular crystal/stone for their healing, either wearing it or carrying it on their person, or other ways (making gem elixirs, etc.).
In the more advanced levels of Reiki training, I teach my students how to set up a particular kind of crystal grid for sending Distant Reiki Healing and how to set up individual crystals that have been cleared, programmed and charged with Reiki to send out distant healing, empower affirmations and more.