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.
"Trevor can't wait to see how much farther he can jump in his new Kangoo Jumps sneakers."
Since Trevor's contemplating physical distance, farther is the right word here. And we hate to be the bearer of bad news, Trevor, but unless those shoes have jetpacks on the back, you're probably not going to notice a big change in your leaping ability courtesy of your cleverly marketed new kicks. But your grammar skills are advancing, at least.
"Further, I can't help but think that you only want to be my friend because I have a pool."
In this (sad) sentence, further is used as a substitute for moreover.
"Before we take this relationship any further, I need to ask you a very important question: Crunchy peanut butter or creamy peanut butter?"
We prefer our peanut butter how we prefer our toast: crunchy. But it's really a personal call. In this sentence, further is the right word because it's referring to a figurative distance. The relationship isn't physically moving anywhere.