1) Get a shovel - you can buy it from John if you get an excavation license

2) Dig a hole. The dirt will stay in the shovel until later.

3) Get any seed with the "Bury" trait

4) Drop exactly 1 seed out of your inventory onto the hole. Make sure the seed in actually in there.
You can either drag and drop from inventory, or press Q from the hotbar

5) Take the shovel out again and replace the dirt into the hole where the seed is.

6) The seed will now be planted, and will grow!

For bags of seeds, instead you'll need to get a hoe from the botanist who will arrive occasionally, and hoe the ground and place the seeds in that.