What is the minimum current I need to supply to a Spartan-6 pin in order to register a high signal?
Assuming the input is set to CMOS mode (you can choose between LVTTL and CMOS amongst others) then almost zero current is required (e.g. a few uA max)
All you really need to be concerned about is the minimum logic high voltage, which will be stated in the datasheet (probably ~3V for 3.3V supply).

The source/drive current for output pins can be set from 2mA to 24mA (see pg.23 and beyond)  

Being pretty complex devices, there are quite a few documents related to these FPGAs, make sure you grab them all and spend a whle reading through them. If you still can't find a particular spec, ask on the Xilinx forum, I've found you get pretty helpful and quick responses there.