In what year did Presbyterianism start?

First, Presbyterian is the name of a denomination (or of a set of related denominations), not a religion. Presbyterians are a part of the Christian religion.

Now as to when the Presbyterian denomination started. Generally it is considered to have started with John Calvin and his preaching and theological school in Geneva, Switzerland. That places it's beginning at 1536, when Calvin published the first version of his influential work "Institutes of the Christian Religion" and was recruited to lead the church in Geneva.