What is Reconstructionism?
Reconstructionism is the resurrecting and reconstructing of the pre-Christian religions of ancient times with as much historic accuracy as possible. Those who desire a recon path spend a lot of time doing research into the practices, culture, beliefs, attitudes, and values of the people who actively lived and worshipped in the past. This can require quite a bit of heavy academic study, but it can also be quite difficult due to the lack of written records from these ancient times.
Rituals and ceremonies are based on those performed in the past, rather than created at the whim of the practitioner. Even then, many of the actual rituals and ceremonies may be too impractical to perform in these modern times. The slaying of a bull as an offering to Zeus is no easy task if you live in a small apartment, not to mention the legal and ethical issues it would involve. Therefore, creative license if often needed.
What Qualifies as a Reconstructed Religion?
As stated above, the religion is of pre-Christian origin, and the reconstructionist approaches his/her studies from the viewpoint of the original culture. It is not "what feels right", or which deities "call to you"; there is no eclecticism or a mixing/matching of spiritual practices.
What Does Not Qualify as a Reconstructed Religion?
Wicca is not a recon religion, because of its relatively modern origins, and the fact that it was created from a combination of other practices. The same would apply to Thelema , a religion based upon a mixture of ceremonial rituals and magicks. Draconic does not qualify, as it is based upon the beliefs regarding creatures that may, or may not, have existed.