Ok, first of all, only Field Supplies are needed to supply any for of base. Player added supplies will reduce downtimes of strats (ammo, fuel, radar etc) by a certain time - IIRC 15 mins. Downtimes of hangars and town buildings can not be reduced with supplies.
Also, supplies need to be from a different base to work (usually troops/supplies are down anyway).
To drop the supplies over the BASE (not town) with a C47, either land the plane and drop when standing still (preferably on concrete, but i think anywhere ON the base is ok. Wait till you see that little "explosion" before towering out.
The other possibility is to drop them from the air (like troops - above 800 ft AGL and under 200 mph).
I usually just land. If i dont have the time to do that (enemies around etc) i come in low and fast, and pull straight up over the base, dropping as soon as im high/slow enough (that way its also easier to make sure the supplies actually drop on the base and dont drift too far).
There only one way (i know of) to check if the supplies were taken. Check your perks in hangar after the sortie (u usually get between 0.5 and 2.5 perks for a supply run).
Vehicle supplies are dropped for friendly vehicles, i think their range is about 800 yds (not sure, maybe someone can confirm?). The vehicle gets a "load supply" button in the upper left corner of the screen. clicking on that repairs the GV as well as reloads all ammo.
Try not to drop those close to enemy GVs as they can load the supplies as well.