I remember going through this quite vividly, mainly because it wasn't that many years ago, but also because I found it to be one of the most disheartening experiences of my life.
My degree course was so intense that I never gave a serious thought to what I might do after I was finished. I just thought it would magically work itself out, like so many graduates do. I'd already undertaken quite a bit of work experience (sandwich course), however, nothing prepared me for graduation and the thoughts and feelings I'd have once all those years of higher education were over (5 in total). My personal dilemma was that I no longer wished to continue on the same path...that was a stressful realisation in itself. Once my course had finally finished and all the exhibitions were over (I studied design) all I wanted was to feel free again. After taking that time, the panic set in as I embarked on the very difficult journey of finding myself my first job.
Presently, my 21 year old niece is going through the same phase in life. Post-graduate FREAKOUT. The best advice I could give to any soon-to-be graduate who hasn't thought about their career is to do something about it early. Get a plan in place and don't assume that just because you're a graduate it's going to be easy - it's not. As a graduate, I really knew nothing about the job market. I was applying for jobs which were totally out of my league because I simply didn't 'get it'. Utilise the careers facilities at your university and get the best advice. Sometimes, simply knowing that you'll be taking a break post-graduation is good enough to eliminate some of the dramas associated with this period of limbo.
Check out this article in The Guardian which explains why leaving career planning until after university is a short-sighted decision:
As the first university students celebrate the end of exams, many will now be thinking about their careers and whether to apply for part-time jobs or work experience over the summer. Though students are now more worried than ever about finding a job after graduation, recently they’ve been told to focus on their studies. In April, Mary Curnock Cook, the former head of university admissions service Ucas, warned students against an “obsession” with careers, saying that undergraduates should not worry about finding a job while studying for their degrees.