Foutre is the vulgar verb, it can mean many different things depending on context, but it is never safe to say in polite contexts.
According to larousse, it can mean
1. to know someone carnally (so to fuck?)
2. to throw with violence, to put, to give, to go
3. Faire, but only in a negative or pejorative sense
Here are some common phrases using foutre-
Je m’en fous- I don’t care, I don’t give a shit (remember this one if you forget all the others, this is the most common way to say I don’t care in french)
Va te faire foutre- go fuck yourself
fous-moi la paix- leave me alone, give me a break
.Foutre dehors- to kick out, throw out.
Se foutre de quelqu’un- to screw / mess / fuck with some one
je me fous de toi- i’m screwing with you
rien à foutre- nothing to do.
Don’t be afraid if you are still confused. Personally I doubt that I’ll be able to grasp all the nuances of foutre, but I understand it when it’s used and that’s an achievement