Crop quality has ten different levels from half a star, all the way up to five stars. The base quality will be what the quality of the seeds are, which are a half star when you first start out.
In order to improve quality, there are several things you can do:
- Use better fields. When you first start out, you only have Gravel Fields, which aren't very good at all. As time goes on, you will gain blueprints that allow you to build better fields.
- Use fertilizer every day to grow better crops. Each bag of fertilizer costs 100G, and is good for a single use, on a single crop. You'll need eight bags of fertilizer to fertilize a whole field. For best results, apply fertilizer every day. I believe it takes ~4 days to improve crop quality by half a star. This may differ for each crop; I will test and make notes as I am able. Field type probably also plays a part in it.
- Important: Do NOT water it more than once a day. You can water crops twice a day, which will make them grow faster. This will adversely affect crop quality, because you won't have as many opportunities to apply fertilizer to improve crop quality. This is especially important for crops you intend to enter in the crop festival.
- I suspect one of the later buildings will allow you to convert a harvested crop into a bag of seeds at the same quality level, ala. Harvest Moon DS. I have no proof, however, so take it with a grain of salt. If it's true, though, it should allow an eventual permanent five stars of all your products.
There's nothing in the tutorial that says anything about decreasing crop quality, but I bet forgetting to water them and allowing them to wilt will decrease quality; otherwise you could just keep it on the brink of death, and feed it fertilizer every day, until you were at the end of the month. Decreasing crop quality when wilting makes sense, as a counter to that. I have no real proof that that's how it work, though.