Question about remote control

[Gizmo]

Hey guys,

I was just researching how remote control software works using Google and can't seem to find a logical answer that makes sense. I regularly go into my school network using it and was wondering how it does what it does. The confusing part for me is, that say for instance you've left your computer running at home and you want it to be switched off. Coincidentally, you're at your work machine and you remotely access your home machine and shut it down. I'm guessing you need to tell the software the public IP of the network that the computer exists in, that you're trying to access, and perhaps along with it's public DNS name, right? But what if the public IP is dynamic and regularly changes? Also, because you're only trying to access 1 computer, you'd have to tell the software it's private IP, right? But what if that is also dynamic and regularly changes? How can you remotely access another network or single computer on a network without having to deal with any firewalls? Or is that what virtual ports are for? To bypass the firewall? Lol, I apologise for the handful of questions, but I have to kill the curiosity

TIA..