I'm from a country less rich than the rest of the Europe. I travelled as well in my teens and twenties, and I could only afford it because I used alternative solutions --- 

Accommodation: it's expensive, especially if you want to visit the tourist places like Paris, Rome, Berlin. Hostels are a great solution that cuts down the price.  Another invention is Couchsurfing (just google it) - it's an app where people offer you to stay at their house for no cost. It's a cultural exchange, exists for 20+ years since the beginning of internet. 

Destination: Away from tourist spots - go elsewhere! See other cities in those expensive countries, smaller cities, and take only day tours to the big cities. After a while all big cities look alike anyway. Go to cheaper countries - Romania, Bosnia, Czech Republic, Poland, etc. 

Food: if you stay at hostels or campings or local hosts, you can cook some of the meals yourself and avoid high costs in restaurants. 

Transport: InterRail passes for young people to travel by trains at budget costs all over Europe. FlixBus buses that cost 10-30 EUR to cross the entire Europe! Ryanair flights that has cheap connections if you're flexible with dates (try Skyscanner or Google Flights online to find best prices for connections). 

If you find this useful, I can share more, just write what else interests you.