According to Wikipedia:
The time and type of fast is generally uniform for all Orthodox Christians; the times of fasting are part of the ecclesiastical calendar, and the method of fasting is set by the Holy Canons and Sacred Tradition.
Sacred tradition could mean just about anytime (well, within reason...), but I found some things on fasting within the Orthodox Canons. In the LXIX Canon from the 85 apostolic canons:
If any Bishop, or Presbyter, or Deacon, or sub-deacon, or Anagnost, or Psalt fails to fast throughout the forty days of Holy Lent, or on Wednesday, or on Friday, let him be deposed from office. Unless he be prevented from doing so by reason of bodily illness.
Since this canon (to the best of my knowledge) dates 'from 375 to 380 AD'1, we can say that the Wednesday and Friday fasts and Holy Lent were already established by that time.
One thing I might mention: I would be wary before I just went and read through the Canons of the Orthodox Church, looking for a certain thing (even if I used a search feature), because now-a-days, the Canons are really meant to be interpreted only by Bishops and clergy, and they are considered "more like guidelines anyway" by most people.
To continue where I left off, when I use my reasoning (uh oh...) it seems to me, that fasts such as the Dormition Fast, Great Lent, and The Nativity Fast would have been established much earlier than that specified date. Why? For instance, picture what would have happened after the death of the Theotokos. Personally, I can picture the Apostles reverently commemorating her repose every year, and gradually deciding to fast before that date... Not sure if that seems like logic to anyone besides me...
Well, that's all I have for now... If I learn anymore I will certainly update this answer.
For a little more on the Orthodox Fasts go to this link. Has about one sentence under the history, but oh well.
Also interesting to note is why Orthodox normally fast on Wednesdays and Fridays (Wikipedia):
In addition to these fasting seasons, Orthodox Christians fast on every Wednesday (in commemoration of Christ's betrayal by Judas Iscariot), and Friday (in commemoration of Christ's Crucifixion) throughout the year. Monastics often fast on Mondays (in imitation of the Angels, who are commemorated on that day in the weekly cycle, since monastics are striving to lead an angelic life on earth, and angels neither eat nor drink).
Perhaps those also were established early on...
Here is a link to the version of the Orthodox Canons which I used in my Answer.