You don't actually need to give a reason, at-will means you can be fired without cause.
For those abroad, remember that most of the time health insurance is tied to employment in the US... so when you get fired your costs also skyrocket (especially if you're the insurance source for your family).
Here in South Africa it's challenging but certainly not impossible. If you provide 3 or so written warnings and set up sessions to try to allow the employee to improve, you may go ahead and dismiss the person. But you can't simply fire at will unless it's gross misconduct or similar.
But is that at the will of your direct boss or there is a process that they have to go through? Like, if for some reason I piss off my manager, they get mad and fire my ass on the spot? How common is this in tech companies?
Pretty uncommon at tech companies, but it's entirely based on the company's policy. The company can fire you at any time (as long as it's not one of several specific bad reasons like racial discrimination), but it's the company that employs you, not your manager. So only the company can fire you.
Generally big tech companies don't give your manager the authority to blindly fire you, but only because that's a decision the company made.
Short answer is yes. Long answer is yes, but reasonable companies will try to find some reasons first as firing for no reason will only increase company's unemployment insurance.
For those abroad, remember that most of the time health insurance is tied to employment in the US... so when you get fired your costs also skyrocket (especially if you're the insurance source for your family).