Could someone please give a simple overview of how mRNA vaccines work?

I have heard explanations on the radio and done Web searches, and it still does not make sense. I get that mRNA carries instructions from DNA to make proteins. Which DNA does the virus use, its own or that of the host? If mRNA is only a messenger, doesn’t that mean that it is the DNA that is in charge? Is the mRNA doctored somehow to keep the virus from creating all the proteins needed to reproduce?