What would you do as a parent if you catch your adolescent son or daughter kissing a boy or girl you don't know around your child's age.?

Ask them about the person. If they have been talking to/with them for a while, and were just scared to tell you(and the other person didn't seem to be a bad person), I would just tell them that they have to tell you about these kinds of things. Also, it depends on the age. If the kids are around 16 and up, this is normal, and is nothing to be worried about. If you feel you must, monitor their actions and be careful they don't end up in an isolated room/house for an extended period of time.

Age (that you did not state) would be very important to decide what's appropriate. And son or daughter might get different reactions.

Tell them no more dating.
I wouldn't have even let the child date until age 18

I would calmly ask the other child to leave the premises, afterward, I would calmy ask my kid why they were kissing, let them explain. But otherwise, I punish harshly so they would get the belt to the butt for that f-ck sh-t, but depending on you, yeah know ground them, whatever, they need to be punished though, as they went behind your back. After that tell them you're not seeing them again, but as you know that won't make it happen, so you'll have to threaten them, with punishment, something will happen if they keep it up, check their phone at random times during the week, do NOT tell them you're going to check their phone, they'll delete the messages if you do, if they're still contacting, you'll know it's them by the messages, if they still are though, then follow through with you're threat and eventually they'll undrstand it's not worth it. Be calm during the entire thing, do not act on anger, act on knowing you have to raise your kid. Never act on anger.