This is a distinction you may find yourself coming back here to review.
Farther refers to physical distance: Los Angeles is farther from New York than from Chicago. I walked farther today than I did yesterday.
Further refers to time, degree or metaphorical distance: Nothing could be further from the truth. Let's look into this further. The harder I try, the further behind I seem to get.
The same rules apply to farthest and furthest: Five miles is the farthest I can run in one session. That's the furthest thing from my mind.
Occasionally, it isn't quite so easy to decide which word to use: I read further into my new book today. Did I get through more pages, so it's a physical distance? Or did I get further into the story, which is a figurative distance? The good news is that when the distinction isn't clear, most authorities say it's okay to use either.
Most of the time, however, you can tell pretty easily if you're writing about an actual distance or not. You'll sound like a grammar pro if you use these two words correctly!