Hmm, this is a little bit very broad question. In a nutshell, no, they don't form in any recognizable modern form until nearly a thousand years after the conventional fall of the Roman Empire. Of the countries you've mentioned, Portugal and England are probably the first two to emerge into polities we would roughly recognize as the ancestors of the modern states.

As for how they emerged, well you could (and plenty of people have) spend lifetimes trying to answer and explain that, but it encompasses basically the entire medieval period. Chris Wickham's The Inheritance of Rome is the best and most accessible book I know of which gives an overview of the development of Europe after Rome.

There was actually a very, very interesting episode of the AskHistorians podcast dedicated to this period and how things developed. It doesn't quite go up to the full development into predecessors of the modern European countries (which took a long time), but I found it a very enlightening resource on the early parts of this process myself: http://askhistorians.libsyn.com/askhistorians-podcast-054-east-and-west-after-the-fall-of-rome