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.
They typically connect to a fueling duct that connects to all tanks. The details vary for different aircraft makes, but a typical arrangement is to have a fueling console next to an under-wing fueling port. The console has a gauge for each tank and switching that allows the fueler to open valving that will allow fuel into each tank from the pressurized fueling duct until the tank is filled to the desired level. Some aircraft will have two fueling ports—one under each wing—that will allow fueling from a second source simultaneously, but they both feed the one pressurized duct.
There is no standard fuel distribution scheme that works across all aircraft models. However, there is great similarity in how it's done, and typically for the same model of aircraft, the tanks will be filled per the same schedule almost every time for a given amount of fuel.
is there a standard fuel distribution that has to be done to every tank for weight/balance reasons?
That it be done right is critical for proper weight & balance, and sometimes fuel is used for balance purposes. For example, let's say you had a tail-heavy load in a 747 freighter such that the zero fuel weight c.g. exceeded the aft limit. If you put fuel in the center tank and consider that fuel as ballast, you could bring the zero fuel weight c.g. within the limit since the 747 center tank c.g. is the most forward of the 747 tanks. And, of course, you have to be careful to not burn that ballast fuel.
If you want to explore fuel loading on a 747-400, go to 747.terryliittschwager.com, select the first aircraft, N402YY, and give it fuel.