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
give item_suit, needs
sv_cheats to be enabled), which causes your health to be visible.
In Portal 2, issuing
ent_dump player after being shot at by a turret displayed the following, so it's pretty safe to assume that it works the exact same way as in 1:
] ent_dump player [...] max_health: 100 health: 10 [...]