Welcome to our Forum, Clairebear.
The ability to fertilize comes at level 3. Weeding comes at level 2. You can increase your gardening skill by reading skill books, taking a class, or by planting more seeds. One tomato plant won't give you any real experience because you just have to water it every day. If you plant more seeds/fruit, your Sim will take more time taking care of them and will gain skill points faster.