How do vaccines work?

I'm loathed to admit that I know people that still think the covid jabs kill people and they probably still think covid was fake... 6 years later. Unfortunately I can only argue so much because I'm a layman and only have a rough idea of how vaccines work. I know nothing in them stays in the body, it's just a weakened version of the virus but maybe someone more medically minded can give me a proper argument.

Because of course every person that dies now (Including Bonnie Tyler) who's had the jab it's obviously because of the jab and nothing else. People in old people homes are dying.... fancy that... because they had the jab. Young people that die...jab. Me I've had the jab, 3 in fact and I'm fine but these people Know better so my days are numbered and if I got hit by a bus tomorrow it would definitely be because of the jab.

Back on a more serious note though what do anti vaxers do when they go into hospital? Refuse treatment? After all who knows what the doctors and nurses are sticking in them? At least no ones saying they cause autism anymore lol.