Skyscanner is a good site for finding budget and other flights in Europe. http://www.skyscanner.com/ However, the trains are often an excellent way to get around. There is an excellent site for train travel here: http://www.seat61.com/ . This includes details of railpasses vs individual tickets. How to select and use a railpass if it;s a good deal for you and links to the various national rail systems in Europe where you can find schedules and prices.

Just book flights to cities you want to visit. Use a travel agent if you are not used to travelling abroad. But, in Europe, the train system is far more efficient than flying and you will be travelling from city centre to city centre, so more practical,

Most use Airplanes. You can go by balloon or hang glider.

Just like in any other place in the world you can look on travel or airline websites for flights from one place to another. Have your passport and possibly a visa.

Enjoy your flight.

Ryan Air.

Plane

While you can try flapping your arms really hard, this will only count as exercise and not get you very far.

Airplanes are the better option.

expedia.com