Minecraft wiki entry for Kelp_farming, associated text: A helmet enchanted with Respiration can allow you to stay underwater for longer. Such a helmet allows for up to an entire minute of time underwater. A Turtle Shell helmet would also be helpful as it allows you to instantly recover air when breaking the surface.
Moving underwater can also be slow. This can be helped with boots enchanted with Depth Strider. A Riptide trident may also be helpful. If mining out an area for a farm, you may also want Aqua Affinity.
Some potions can also be helpful. A potion of Water Breathing can allow you to stay underwater indefinitely and a potion of Night Vision can allow you to see much better.
A sword with Smite may be helpful for fending off Drowned.
Using Ice to create Water Sources with a Silk Touch Pickaxe is more convenient and effective than using water buckets to place water.