History of Reiki
It is believed Reiki as we know it was established in the 1800's. Dr. Mikao Usui, also known as Usui Sensei, began what he considered a way of treating people by laying hands on others.
Dr. Usui sought for a treatment which was not attached to religion so that all would be able to access his healings. He also taught others so that they could share the healing freely.
It is said he went on a retreat to the mountains for 21 days and during that time of fasting, meditating and prayer, he received a vision of Reiki and the healing symbols which came with it. Once he returned from his retreat he began to use Reiki on those who needed it and also to teach others, including Dr. Hayashi who went on to further develop the Reiki system of healing.
Reiki further developed in the mid-1950's when Hawayo Takata also learned Reiki. Once she moved from Tokyo to the United States, she modified Reiki to be a bit more 'Western' and began teaching her students that way.
Today there are many variations of Reiki including the healing symbols (which are drawn in the practitioners hands or in the air during sessions). Other variations are how long someone needs to train for, how long to wait in between receiving different levels and prices to charge for services rendered.
One thing remains consistent though: Reiki is considered to be healing energy always working through intention and for the highest good. So really, no matter how you draw those symbols or place your hands, your intention and understanding of what you are asking will help facilitate Reiki healing.