Studying is not a cheap hobby you start without considering how to finance it. One important matter of expense that you have to take into consideration are the tuition fees that most European countries charge.
Depending on where you live it can pay off to take a look at your neighbors education system as some countries like Denmark do not charge these fees for EU-students. In Denmark you can even get the national public funding grant as an EU-student when you can prove that you have a job placement of at least 12 hours/week.
Another matter that you should keep in mind and that varies a lot among different countries are the living expenses. Most Scandinavian countries for example have rather higher costs of living. Besides tuition fees and costs of living, initially if you start your studies a complete basic equipment of books and material is needed (i.e. a computer and office equipment) and perhaps an apartment with the necessary furniture.
Then, of course, there are the costs for insurance, clothes, food, trips back home, leisure time etc. The German students association has researched the cost of living for students and found these to be approximately between 7.000 9.000 Euro per year (that makes 550-780 Euro per month).
You see, starting your student life should be well-planned.