Give your contractual notice, whether thats 2 weeks in the US, or a month or 3 months in the UK or whatever and be prepared to actually leave at the end of it.
Any other advice is actually harmful to the majority of people.
72 hours notice in some states if you want to be paid out for everything they owe you on the spot.
But otherwise I give them about as much notice as they would give me: at 4:59PM on Friday I send an email to HR informing them that today was my last day.
Severance is never paid unless you sign away your rights.
There is no contractual requirement for severance.
We are at will slaves.