Example 1
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.
Example 2
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.
Example 3
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.