Fire ritual is found in many ancient religions, including Hinduism, Zoroastrianism, Buddhism, ancient Greco-Roman religions, American Indian religion, Inca religion, Mayan religion etc. Fire is a representative of god on earth. Spending time worshipping god through fire purifies one's subtle consciousness. That happens because the internal fire responsible for purifying one's consciousness resonates to the external fire.
Dr Manish Pandit is from Pune and works in Birmingham, UK as a nuclear medicine expert. He is a disciple of Nakhate Mahraj in the lineage of Sri Vasudevananda Saraswati (Tembe Swami). The idea of spreading homa in the world was revealed to him in a dream a few years ago, in which he saw eight elevated beings. They transported him across blue skies to Chennai, India, where he was shown the big fire that was to be lighted in the world in future. They told him to start the work. They assured him that homa as a spiritual sadhana was very appropriate in Kali yuga. As spiritually inclined people have fewer and fewer hours to spend on spiritual sadhana everyday with the progressing Kali yuga, sadhanas that work fast are more relevant. Homa works much faster than japa and other spiritual sadhanas. They told him that the practice of homa would transform into a movement that would reach across caste, class and race barriers.
In March 2006, Dr Manish Pandit and PVR Narasimha Rao travelled to Chennai, India and performed a Shata Chandi homa at the Kalikambal temple there, with the help of Swami Satha Sivom (a traditional Sivacharya and head priest of the famous temple), with a sankalpa for relief from legal troubles to Swami Jayendra Saraswati (Shankaracharya of Kanchi).
During that event, Dr Pandit had a darshan of Divine Mother on a Friday and was reassured by Her about the right course of events regarding spreading homa in the world. Starting from that Shata Chandi homa, a chain of events led to the preparation of various homa manuals. Thousands of spiritual seekers interested in homa are performing a homa by themselves using these resources.
Based on the guidance received, this movement is expected to grow further in coming years.
Detailed manuals giving short procedures for doing various types of homa or havan (fire ritual) are available here.
There are regular manuals for performing homa to some deities and the "simplest" manuals for many more deities. One should realize that "simplest" homa is not inferior to "regular" homa. Some people like elaborate rituals and some people like to simplify the ritual and spend more time focusing the mind of God. Both approaches are fine and one should pick what suits one.
There are some MP3 audio recordings and video too. You can use these resources to perform several kinds of short homa by yourself. More resources will be added in future.