first buy a seed, then buy a pot from that guy by that dragon cave place, then go home, place your pot and finally place your seed in your pot. ( every seed needs a certain pot) ( you can use seed spells to help your plant grow, and you can buy them from the same guy that you bought the pot the pot from )
At level 12 you can visit the Life school to get you started, you will be given seeds and visits to the gardener, blossom etc. that will help you understand how it works.
In your dorm you are given 2 small pots to plant in if you want to start there. As you progress you will find you need to go to the gardeners for more spells for your garden care such as Bees, mist, music, sun light and pest control spells. Once plants are planted they can not be moved so before you start make sure they were where you want them to stay for a while.
Each seed tells you what size plot or pot it needs. You need to level up in order to plant higher level seeds.
Decorative pots only come small to medium, plots or soil is small to large, there are also plants that require enchanted soil.
I find it best to start with 1 or 2 dandelion and see how it's done and branch out from there. In no time you will be able to plant more seed types.