What you need
You need a hoe and seeds. A recommended addition would be a shovel for digging chanels of to keep the plants watered.
To start farming equip your hoe, stand in front of grass and hit action until you tilled it. Now stand on the tilled ground and use the desired seed.
From this point on you need to wait a certain amount of time until your plant is fully grown or withered, after which you can harvest your crops.
Watering plants and increasing your farming skill will improve your chances of plants growing successfully. If a seed is planted next to a water tile it is considered watered. This is easier than using a bucket. You will always get a seed back from a plant even if it failed to grow and withered. You might want to dig a channel of water to plant a row of seeds next to. When a plant grows it has a chance to dry up a nearby water tile depending on your farming skill.
Withered plants and aloe act like normal items and despawn.