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I am planning to go to Europe this June. Entry country will be Amsterdam. I am not familiar with Europe, is it easy to just take trains and buses across? Since I want to go to Belgium, France (Strasbourg) and Paris. Anyone can propose an itinerary, how many days would I need? Are there cheap hotels ?

Yes
No, not really and yes.

Public transportation in Europe is extemely easy.

How do we know how many days you have, what you like to do and what your interests are? This is a good time for you to get a book. We could rewrite every travel book on the shelf but why? Please do some research. There is great information right here on this site.

What's does "cheap hotel" mean to you?

You should post this on the Europe board.

But first you should do some reading - try Rick Steves' "Europe Through the Back Door" and Lonely Planet's "Read This First Europe". Also look at Exploring or Insight or Eyewitness guides for the countries you're interested in to decide where to go.

For cheap flights in Europe see whichbudget.com, for train schedules see bahn.de and for train travel in general see seat61.com, I don't usually take long distance buses.

I agree, please post on the Europe forum (use the drop down menu at the top of this page under "Change Forum".

It is helpful to name a price range for your hotels. Cheap means different things to different people. Are you willing to stay in hostels? Or you want a hotel?

I agree with the guidebook suggestions above as a place to start planning.

You need to buy some guidebooks and maps, and do a rough plan of what you want to see and where you want to go. Then go to the Europe forum with more specific questions. Tripadvisor is also a good website for hotel reviews.