Okay, if you want to complete this quest here are two things you need to know right from the start:
one - you'll need to be fairly on the ball about checking up on this quest for a full thirty minutes of real time, and
two - If you mess up, you'll need 10 ash, 10 demon weed and 10 zinc sand to trade for another one.
Anyway, once you've opened your one-off planting pack, you'll see it contains a pot, a special fast-growing seed, some water and some fertiliser. Now you need to go into your house and place the pot down somewhere using your place furniture function. Then click on the pot - a little menu will appear. Drag the seed into the window at the top to 'plant' it, then drag the fertiliser and water into the corresponding windows below. Hit the buttons to fertilise and water.
Near the top of the menu, on the left, is a face icon. The figure beside it starts off at 100%, and this goes down as time passes, but as long as the face icon is smiley you don't need to worry too much. To the right of that is a plant pot icon; this starts at 0% and goes up for each unit of fertiliser and water you give your seed. You now have two choices; you can either feed and water your plant until the plant pot figure reaches about 25-30% and then stay in the house and keep a vigil on it for thirty minutes, topping up as necessary. Alteratively you can load your entire contents of both water and fertiliser onto your plant, taking the plant pot figure up to at least 60% (this may involve going out and buying more water and fertiliser from the plant supplies vendor) and then go back out and quest for a while - remembering to come back when the thirty minutes is up. Whichever option you choose, at the end of thirty minutes you should have succeeded in growing a pretty plant. Harvest it by hitting the button at the bottom-left of the plant menu. And then you're done! Take it back to the Planting Teacher, and then she'll give you your reward: another planting pack with seeds that take a full two days of real time to grow. Oh joy.....isn't planting fun?