From DarkSpace WIKI
Damage, system failures, and ammo shortages are a fact of combat. Supply ships are there to reverse the process, turning derelict hulks back into fighting warships. Supply ships can replenish ammo, refuel jump drives, repair armor, and fix damaged or destroyed systems.
Supplying Your Allies
To supply a ship, you must close to within 250 gu, target them, and then activate your drone bays ( "Y" ).
You will notice drones with green trails leave your ship and surround the target vessel. These drones can be left behind when jumping, but that will not affect your ability to perform repair operations, you will simply not see the green drones during repairs. If at any point you or your target move out of range, the repair/reload process will automatically stop.
Should you wish to self-repair, hold the Shift key and then activate your drone bays. Please note that repairing allied ships will add to your prestige, but repairing yourself will not. Effective use of supply ships will often turn the tide of battle.
Restocking supply drones
When you run low on drones (or run out completely) you can orbit any friendly planet to restock your supply of drones. Flying near supply platforms will also restock these drones.
Flying a supply craft is a very prestigious profession, second only to combat, since everyone loves to have a supply ship following them. Although they are small, supply ships can be very resilient, making them good for new players to gain experience quickly at low ranks.