Um, yes, of course you have to ask for time off. How else would it work - you'd just tell your manager that you weren't coming in and then not show up and your tasks wouldn't get done? That seems ludicrous, you'd be fired, good luck getting anything you left in your desk drawers back.
I'm fortunate now to work at a place where if I had to take time off for a medical emergency or paternity leave I could call and explain and it would almost definitely be granted, they might ask for some email support or phone calls to offload my tasks to someone else... but you still have to ask.
> you'd just tell your manager that you weren't coming in and then not show up and your tasks wouldn't get done?
Yes, exactly. That's how it works in my organization. You don't schedule tasks when you're going to be out of the office. If they're time critical, someone else will pick them up (and drop less time critical tasks of their own). If they're not time critical, they just wait for your return.
I recognize that I'm lucky to be in this situation, but it's certainly possible if you have a reasonable bus-factor.
I'm fortunate now to work at a place where if I had to take time off for a medical emergency or paternity leave I could call and explain and it would almost definitely be granted, they might ask for some email support or phone calls to offload my tasks to someone else... but you still have to ask.