How do you apply for new jobs while working full-time?

I’m currently working almost full-time and I really want to start applying for new jobs, but I’m struggling with how people actually do this in practice.

Most job interviews seem to happen during regular business hours… which is exactly when I’m supposed to be at my current job. I don’t want to raise any suspicion with my employer, but it also feels nearly impossible to schedule calls or interviews without making it obvious that something’s going on.

For those of you who’ve changed jobs while still employed: How did you manage it? Did you take time off? Pretend you had appointments? Ask for early/late calls? And how do you handle multiple interview rounds?

Any tips or strategies are really appreciated. I’m sure I’m not the only one struggling with this but I’ve never seen a clear answer.