Travel to Europe at a Low Cost

My hope for next year or or so, is to travel to Europe.

I have never been to Europe, but, some of my friends have been to Germany, Croatia, Spain and other countries in Europe. They traveled by train or airplane at a low cost, but, they also tell me that travel by airplane is more expensive than travel by train.

What do you think? Is this true or false? What advice can you give me? What train should I take? What city or what country should I visit? What hostel should I stay at?

I think I may want to visit to Italy or more specifically the towns of Mascherata and Udine. Afterwards I would travel to different countries in Europe by train. I will have to find out which trains to take and which cities in which I have to make connections. 

What is your advice? Should I make the trip in the summer or winter and which countries should I visit? Do you have any suggestions on which Hostels to stay at?

I would appreciate any help you can give me.

Thank you for your time.