do I begin with a lot of fluff about how I learned so much in their class and really liked it or do I just straight up ask?
Come prepared. Write up a resume and a brag sheet specific to that teacher. Come up with 4 or 5 words that you would use to describe yourself - outgoing, helpful, studious, intellectual, funny, serious, bright, intuitive, hardworking, etc. Let them know what themes you will be using in your essay; if they choose to incorporate those themes into their letters it helps give a unified feel to your application. Think back on the time you spent in their class and try to remember if there were any incidents where you helped other students, or where you got a very good grade on a particular project or paper or test, or where you showed yourself a leader on a group project. Write those down.
If the teacher sounds at all reluctant about writing a letter for you, go to another teacher.
It should be a class you are doing well in…You can just ask if they would be able to give you a strong college recommondation?