Eurolines is a bus company that runs through Europe. It's usually pretty cheap, but sometimes the train price is about the same. You can check their prices online.
A lot of the cities you're going to are very touristy, so if you're going in the summer, expect lots of crowds and things being overpriced. Of course you can do things cheaper, by shopping around (get out of the really touristy areas to eat/ drink, buy groceries instead of eating out, don't buy souvinirs in the really touristy areas, etc).
Staying in
hostels can be a lot cheaper, especially if you book ahead. If you have a semi firm itinerary in place, you can get things booked, so you're not looking for a room at the last minute and paying much dinero. It's a cheap deposit and you have a guaranteed room.
Flying from city to city can be cheap on flights like ryanair.com, germanwings.com, wizzair.com, etc. There are a lot of low budget airlines, so make sure to shop those for inter-Europe travel.
Getting there doesn't have to be as expensive as you might think, even if you're flying in the summer. Don't eliminate flying into places like Dublin or London. You can usually get a cheap flight to the mainland from either city (if you do hit London, easyjet.com is based in England, so it's another cheap flight site).
Search!! Don't just settle. Good sites are sidestep.com, aerlingus.com, studentuniverse.com, etc. I found that booking about four months in advance was ideal.
Make sure you have an atm/debit card. You get the most current exchange rates, you don't have to deal with much cash, and they're just so handy. Plus, if you have online banking, you can track your spending and purchases.
Good luck.