In Portal (and Portal 2), I can get hurt by lasers, bullets, etc. Do I have a finite amount of health that is depleted every time I get singed, or is it a case of sustaining damage for a continuous amount of time resulting in death?
You do have 100 health, only the exact number isn't shown on the HUD.
Continuous damage will kill you, but your health fully regenerates very quickly when you aren't damaged for a bit.
You can observe this in Portal 1 by giving yourself the HEV suit (console command
In Portal 2, issuing