Keep them warm and to feed them as follows…
Small ducks need warmth (they can’t supply it themselves). You need to buy or make a “brooder” for their warmth and protection.
To make one yourself, get a big box and hang a light bulb in there that is close enough to give off some heat but not so close that the little guy can get burnt. Don’t let him touch it. The box should be big enough so that the little guy can move closer to the heat when he is warm and move away from the heat when he is too hot. He’ll find his own comfort level. Always be careful about placing lights and electrical wires safe and secure to prevent fires.
The best “bedding” is an old bath towel. Don’t use hay or straw. It just sticks to them and is harder to clean. Don’t use newspaper either as they tend to be unable to get their footing and sometimes this causes “splayed legs” (Good footing when they are small helps their legs to develop more properly).
Since ducklings hatched in captivity are separated from their natural mom, they should not be placed in water for too long at all and especially without constant supervision. Instinctually they love playing in the water, but since their oil glands are not able to produce enough oil to keep them afloat they’ll drown easily. In nature baby ducklings get their water resistant oils from their moms until they are five or six weeks old and their own oil glands begin to function. The bottom line is that baby ducks love to swim but without mom around are vulnerable to drowning and chills. They don’t need to swim to survive at all.
At the same time, baby ducklings do need lots of water with their food as they must have water to swallow. Due to the issues in the previous paragraph, you must devise a way for them to drink lots of water without diving into their drinking water. They can drown in that too. The best method I’ve ever seen is to cut a small hole in the side of a plastic milk carton that is big enough for them to put their head into but make the hole too small for them to jump through it. Then fill it with water just up to that hole. You’ll have to change the water often as they will dirty it up daily (with food). You may have to teach them how to find the water in the beginning by pushing their heads in their a few times but once they figure it out, they will go back and forth between their food and water constantly. Once they start eating it seems like they never stop.
Regarding feed… go to a local feed store and ask for “unmedicated chicken mash”. Basically this is mashed up chicken feed. It is important to ask for “unmedicated” brands as ducklings eat a lot more than chicks and will poison themselves on the medicated brands. They don’t need the medication like chicks do. They actually can be quite hardy once they begin growing up.
Lastly, remember that you are your duckling’s protector. The most common cause of death in pet ducklings (and ducks for that matter) is an attack by a predator. Ducklings have no real defense mechanism and are vulnerable to pet dogs or cats or a stray neighborhood pet. You need to be conscious of any animals around their environment and keen to provide protection. It only takes a few seconds for a playful larger animal or predator to kill your ducklings.