This question can be asked at different levels of generality. “It is raining,” you may say; or, “The climate is warming.” You may know it is raining because you have just been outside or you have looked out the window or you have checked your weather app. You may know that the climate is warming because you kept careful records of the daily temperature; have reviewed the scientific literature on climate; or simply because you have kept up with the news. Philosophers ask questions like, “How do you know you are not dreaming?” or “How do you know there is an external world?” Your answers here will be different and will often not satisfy the philosopher anyway. Finally, we may ask my question: “How do you know things?” That is, how do you go about acquiring knowledge. The answer may be, “Through experimentation and observation,” or, “through reading and conversation,” or of course little bit of both.
When you are writing in an academic setting you should mainly be saying things you know. And, as Wayne Booth and Herbert Feigl remind us, you should try to explain to your reader how you know. You should give your reader the same reasons you have to believe, understand, or agree with your claims. That may not immediately work; the reader may not instantly believe you, or understand you, or agree with you. In fact, you should count on that not happening too quickly in most cases, but your job as a writer is to tell the reader what led you to think as you do. Tell your reader what what you’ve read and what you found there; or tell your reader what your data shows; or even just tell the reader how you proceeded from certain premises (that the reader, like you, thinks are true) to your conclusion. Those three sources — reading, experience, reasoning — are probably going to be the main ones. To be honest, at the moment, I can’t think of other ways of knowing at university.
Putting it that way, I think I may just have said something controversial. Maybe I’ll spend this week thinking out loud a little about that.