Logic functions (like hashing SHA256 function) are processed by gates connected in proper way. FPGA is a electronic component called chip with milions of gates and interconnects inside (just like CPU or GPU) but that interconnects between gates are not defined by manufacturer (in CPU,GPU are). You decide how to connect those gates between each other and in a result what function that FPGA will perform. You are doing this by downloading a bitsream to them (you may consider this as loading program). Some boards have some sort of non volatile memory so this process can be automated and loading bitstream wiil occur without user interference. When FPGA will be "programmed" you need to download a data to process. This is mostly done by a PC computer with proper aplication running on it, and dowlading is thru USB. In that aplication you can set a pool, user name,password and other stuff if needed.
Here in forum you can find offers of boards designed specially for mining with program in it, so just plug to computer USB, to power supply, run program on PC, set and mine. Profit.
Advantages of FPGA's are:
-10 (more or less) times less power consumed than GPU with the same hashrate
-less heat
-less noise
Disadvantages:
-price
-almost zero resale value.
Thats a short version of FPGA story