It can vary from university to university, but generally you would be provided lecture notes (slides from the lecture) where you can write down what you want during the lecture. I haven't come across a case where they give you lecture notes electronically where you can write on them during the lectures.
I personally take notes using the lecture notes provided. Specifically, I would normally note down material I am not particularly familiar with or highlight material that's important. I wouldn't want to write everything the prof is saying - it's too much to do in short amount of time unless you're a pro at it. I would focus on the main points and note down things that I wouldn't expect to be able to read up on. Too much notes can usually work against you as opposed to aid your learning.
If by any chance you need to record everything word for word, bring a voice recorder with you (ideally not use your phone for this), check with the lecturer about using it, and then record the entire lecture (assuming there aren't any saved lecture videos on your university intranet available for your use).
According to recommendations by various sources, you can use apps like EverNote or Notion (this has an AI included). However, the note taking app on your tablet is usually more than enough (would ideally like an app that would allow you to annotate, doodle, as well as do text if you want).
The way you should organise your notes is supposedly by topic; you want there to be enough material for you to refer back to, but have the structure fluid enough for you to link to other topics and notes in other areas. Taking notes is one skill, organising the notes so they become useful is quite another.
See the following videos for other opinions:
https://www.youtube.com/watch?v=RfnLqdllftkhttps://www.youtube.com/watch?v=jBHLC8dff48https://www.youtube.com/watch?v=AffuwyJZTQQhttps://aliabdaal.com/the-5-rs-of-note-taking/https://www.youtube.com/watch?v=HuX3yT4rvDs