usually when I debug things my method is sort of a mix of linear and binary search where I start at one place, see if the a value is what I expect it to be, then move along to a different part of the code to see if something is wrong there, reducing the search space and repeating as necessary.
Sometimes my method is instead to look at data output at a certain level of abstraction like system calls (which is usually not helpful except for detecting a network hang or a path config whose directory doesn't exist) or database queries or something. That is usually more helpful if I either already suspect I know where the problem is and need to know what model name or file name to `ag` for.
If (Hephaestus be praised) there is actually an automated test framework in place, I'll start by writing a failing test or copy-pasting an existing test and modifying it to fail, then (if it isn't JavaScript), inserting a debugger into a function the test calls.
All of this tends to be pretty successful.
But I've occasionally found myself on a project where I just have a sense that I don't know what is going on or how pieces fit together and I feel a strong temptation to stop and fix that sense of bewilderment. When I resist this urge is when it feels like I am trying things at random.