When backpacking in Europe, is it difficult to find hostels?

No, you find out BEFOREHAND where they are, get the address and phone numbers and directions to the actual building .... And OF COURSE there are people at train stations you can ask, it's called Tourist Information, the symbol is this big letter I. Find out where hostels are by going to www.hostelworld.com. Unbelievable. Absolutely unbelievable.

Join Hostelling International and your local affiliate (HIUSA in the US), who among other things have online and downloadable directories of hostels all over the world. Rather than just showing up in a city and hoping to find something, your life will be easier if you plan at least a few days ahead and make a reservation before you arrive.

Some general advice: First off I'd check out hostelworld.com and/or hostelbookers.com. You can use them to book rooms in youth hostels practically anywhere, and in general they are a hugely helpful resource. Also, because these websites exist, it's a very good idea to book beds at least a few days in advance, especially during the summer and on Friday and Saturday nights. If you do simply show up somewhere there are often--but not always--tourist information centers that can help you out. However if you show up late, or are going to a small town, you may be out of luck. In general I personally prefer to make reservations at least a few days out so that I know I'll have a bed waiting for me when I arrive somewhere. A guidebook is also a very good resource. Also if you can get an overnight train to a destination you can certainly save yourself a night's hotel/hostel cost. That said you'll probably often not be going between destinations so far apart that you can get a full night's sleep on the train.