Assuming that you have Mathematica installed:
* Open a notebook (<CTL> N) or press the New Document on the Welcome Screen window.
* Click on Format
* Click on Stylesheet
* Click on Utility
* Click on Outline
That will let you take natural language notes.
However: Mathematica has a steep learning curve, even for simple tasks. You need, I'd say, about 8 hours of practice transcribing with the above to develop the reflexes you need to keep up with a lecture. Try taking notes on a YouTube nature documentary, or a presentation with actual formulae if you can find one. If you want to try copying formulae, I'd say you need another 16 hours of practice, 3 work days total. Try working calculus or advanced algebra problems. Unless you get very good (touch typing level), you might be better off using paper and pencil. Becoming proficient involves learning the various editing commands and keyboard shortcuts listed under Edit at to of each notebook file.
If you can become proficient enough, there are some advantages to running examples of the methods listed in the lecture. However, be aware that course problems are a very special case. Varying course problems even a little bit can lead to problems that are very hard to solve, or even to understand, even with Mathematica. Be careful when you poke around the mathematics; you can find yourself in a time trap. Note it and get back to the assigned work. You learn about traps in graduate school.
So: Yes, you can do it. Becoming proficient enough to do it would help very much if extensive work in Mathematica is likely. However, don't walk into class and try to use Mathematica for the first time. You'll lose the lecture and likely your composure as well. You're good or you wouldn't be taking the course, but nobody good enough to go in cold and take useful notes in Mathematica.