Gardening is simple when you learn how. I'll explain how.
Talk to Farley in Golem Court when you are level 12 or higher. He'll give you some quests about gardening. Complete them and earn about 3000 gold. Spend all of it on Farley's Rank 1 Gardening spells.
Go home and in your dorm, you have two pots. Put the dandelion Farley gives you into one of them.
Now the rest of the process is simple.
The plant starts out as a seedling. You won't have to do anything in this stage.
In the later stages of growth, you will have to tend to the plant by getting rid of pests and stuff like that.
It will take a few days for the plant to reach Elder, so check back from time to time.
(Need seeds? Look for them at the Bazaar, or you can sometimes find them by farming off Nirini Sentries in Krokotopia.)