The section that you are talking about is in chapter 8. It covers a few pages, so giving an exact page is not possible, plus I do not know which edition you are reading. Definitely examine chapter 8 though.
The weather is warming up because it is June by this point in the story. Kit is at first excited to go work in the onion fields, because at this point all of the other jobs that she has had are "boring" and difficult in her opinion, including things like cleaning, cooking, sewing, and other indoor "women's" work. Finally, the fields give her a chance to work outside. Kit, being Kit, quickly thinks working on the dirty ground over the onions is just as bad as the other work too. Kit is now beginning to seriously consider marriage to William Ashby because it might relieve her from all of this horrible work.
When the girls return home, Kit finds out that she has an opportunity to help Mercy teach at the one room schoolhouse. Kit is super excited because she feels that she would be good at it, AND she could earn a wage for it. Also, Kit hopes it makes her host family feel like she is contributing in some positive way.