I'm on really good terms with one of my teachers this year (junior), but I know she's a popular choice for recommendation letters. Do teachers place a limit on the number of letters they'll write? When is a normal time to ask for one to ensure that I don't get turned away?
Yes, many teachers do place limits on the number of recommendation letters they will write in any given year. It's more manageable for teachers to write these letters over the summer, so I would advise you to ask your teacher about this within the next month. Junior spring is the best time to ask for recommendations because you'll give your teachers plenty of time to write well-thought-out letters that aren't infused with stress due to application deadlines. If you wait until senior year to ask for a letter, you risk getting a carelessly written recommendation or no recommendation at all. This article should give you some more insight into common high school policies regarding the recommendation letter process.
You only mention one teacher here, but since two teacher recommendations is the standard requirement at most colleges, you should also think of another potential candidate. Ideally, it will be one of the other teachers from Junior year who has a positive opinion of you and your work. You can read this complete guide to asking for recommendation letters if you're nervous about reaching out to a teacher you don't know as well.