I am interested in communicating with arduino over a telephone line. What is the maximum bytes per second that can be achieved? Is fsk the the fastest or are there other methods? Any example links would be appreciated also.
First obvious thing to state is that an Arduino cannot directly communicate over a telephone line. A device called a modem (for modulator/demodulator) is required at both ends of the phone line. How fast a speed can be attained depends on the method and complexity of the modem. You mentioned FSK, I believe the fastest modem speed that used simple FSK is the old Bell 201 standard running at 1200 baud. The fastest modem I'm aware of is the 56K baud modems, however be aware that such 56K modems had to negotiate with the far modem to establish how fast they could actually work for that specific link at that specific time, so frequently, if not mostly, they linked up at lower speeds.