Here's the short version: you use the word farther when you are talking about physical distance and further when you are talking about metaphorical or figurative distance. (For example, if your ex-BFF just spread another rumor behind your back, you might say she fell even further out of your good graces.)
Want a fun Jedi mind trick to help you remember? Farther has the word far in it, which obviously has to do with distance.
Though both farther and further refer to distance in some way, the word further has another significant meaning. Short for furthermore, further can be used instead of in addition or moreover.
You'll find that you can often interchange further and farther, especially in every day usage. But don't you dare try to use the word farther when you really mean furthermore.
Grammarians will bring the pain.