Use 'by far' when you want to highlight something as much more extreme than others in its category. His solution was by far the most effective we've seen.
Pro Tip 2/3
Comparison Required
'By far' needs a comparison; it doesn't work alone to describe a single item without context. That movie was by far the worst this year.
Pro Tip 3/3
Positive or Negative
The phrase can describe both good and bad extremes; context determines the meaning. This is by far the least expensive option.