The easiest way to travel around Europe is by train. You can easily go from city centre to city centre without the hassle of airport security checks and the like. Possibly the biggest dilemma one faces when going via rail is whether to get a railpass or buy point to point tickets. In my experience so far, point to point is far cheaper than the railpass if you buy well in advance.
While the point to point tickets are cheaper, you lose the flexibility to change them. On the other hand, if you shell out the extra money for a railpass, you have much more flexibility but the price per ticket that you’re paying can in some cases be significantly higher than point to point. On top of that, some countries add on a railpass surcharge, may require reservations, and sometimes have quotas for railpass users. Unfortunately, you’ll have to really think about which one works best for you.
For more information on this and train travel in just about any part of the world the amazing website www.seat61.com has got all you need. I used this site extensively to do my European train research.