How do they fill fuel in big aircraft?
My answer is limited to commercial type aircraft (e.g., B737/757/767, etc.).  There is variance between aircraft types.


  Question: when they are filling fuel, do they connect hoses to each tank individually or just connect to one tank? Or is it per side - fill up each side individually.



For most large commercial aircraft (e.g., B757, B767 etc.) single-point fueling is done from one location underneath one of the wings.  This single-point fueling system allows fuel to be 
loaded to all tanks, e.g., Left/Right Main wing tanks and the Center tank (if necessary) from a single location.  The switches on the single-point refueling panel operate pumps
and cross-feed valves to allow all tanks to be fueled from this single location. 







  Question: Also suge/vent tank at the tail end of a380 seems to too high. Do they fill in those tanks too?



A "surge" tank (or similar notation) is normally dry but is designed to hold fuel that passes through the main fuel vents (due to expansion or overfilling) in the normal tanks so that the fuel does not spill out (on the ground) and cause a fuel spill.  This fuel ultimately works its way back to the normal tanks through gravity.





  Question: After fuel calculations are done, is there a standard fuel distribution that has to be done to every tank for weight/balance reasons?



Generally speaking Yes.  The location of the fuel tanks in an aircraft is designed (again, generally speaking) to be near the center of gravity (CG) for the aircraft.  So, as fuel is burned during the flight the aircraft does not find itself outside of the appropriate weight/balance envelope. However, calculations are done to ensure this and verify that the fuel loading at the beginning of the flight results in the CG being within limits and that the CG is within limits at the end of the flight after the anticipated amount of fuel is burned.  Generally speaking (again), the aircraft is designed to stay within limits for most types of operations considering possible fuel, cargo, and passenger loads that may be encountered during normal operations.


FYI - If the single-point fueling system is inoperative for some reason over-wing fuel points allow for manual filling of the main tanks.  Also, should the Fuel Quantity Indicating System (FQIS) system fail and 
the total amount of fuel in the tanks cannot be determined, fuel quantity can be measured using measuring sticks (with a reference chart available to determine (manually) how much 
fuel is in each tank.



Below from ABXtranet.com is a picture of the fueling procedures for a B767 and a picture of the Fuel Control Panel (B767 Single Point Refueling):











Here is the link to ABXAir's B767 Fueling Procedures Manual:
refuel procedures ABXAir