I’ve been traveling primarily by bus from city to city (Eurolines). Costs vary depending on distance, cheapest have been €15 from Irish city to Irish city and as much as €50 from Amsterdam to Berlin. It’s a lot cheaper than train but much slower (and not as comfortable to sleep in over great distances).
Within a city, in Ireland, I used the buses or walked. In France, Belgium, Netherlands, Germany, it’s all about the metro lines (subways). I biked around for a day in Amsterdam, that’s how everyone gets around there but big countries like France and Germany require the use of metros or you will be walking a lot. In France/Belgium/Germany, you can buy tickets at the stations but in Netherlands, everyone uses a pre-loaded access card to scan in/out of terminals. Once you get the hang of the metro system in one country, it’s pretty much similar to the others (at least from my experiences so far). Know what line you need to get on, know your stop, know what direction to go (read: know the name of the end of each line).
Hostels vary from €10-25 for dorms (4-10 beds in a dorm, fewer beds usually mean more costly but also depends on how nice the hostel is, how popular the area is, how reputable the hostel is etc.)
I think for the most part, transportation and hostel fees are a bulk of the cost. Cost of eating/drinking will depend on you. For me, I mix eating street food (€2-4) with the occasional sit-down restaurant (€10-20) and also hostel cooking (€3-6). I don’t drink much so I save there (pint of beer can cost €3-5, cheapest I’ve bought was €1.50 for a bottle of Jupiler).
Museums (€5-15) , tours (€10-20) cost money but I’ve recently discovered the wonderful Sandeman’s Free Walking Tours (Kiera told me about it actually). They are the best thing to happen to a budget traveller. I also enjoy wandering and getting lost and taking out the guidebook to find my way home. Or go sit in some park that all the locals love to hang out at.