Finding the abstraction level
In order to start unit testing, you have to start writing tests; this is what they'll tell you. If you want to get good at it, just start writing tests, any and a lot of them. The rest will solve itself.
I've watched experienced developers sit around staring dumbfounded at an empty screen because they couldn't get into their mind how to get started, what to test.
The question is not unfounded. In fact, it is still debated in the Test Driven Development (TDD) community what should be tested. The ground rule is that the test should bring at least as much value as the cost of writing it, but that is a bad rule for someone new to testing, as all tests are expensive for them to write.
Public interface
Once your tests suite grows into a couple thousand tests, they will start breaking, not only when you change functionality and expect them to break, but when you add functionality or optimize the inner workings of a function.
This is what we call brittle...