What is the cheapest way to travel around Europe in 90 days?
As the others have said, trains are cheap and so are buses. There is a new line of coach buses Flixbus (your bus is → FlixBus) operating in Germany and some parts of Europe (not all) so you really have to check where you are going. Travelling can be cheap but it involves a lot of research so you have to plough through online and the dozens of answers here on Quora.
Stay for free. Travel and accommodations are going to be the largest expenses of that trip. It's possibly and not very difficult. I suggest trying some of these platforms. Top 5 Best Websites That Let You Stay for Free
If you can't find a host on there, try using AllTheRooms to see everything available under your budget.
Getting a Eurail pass and staying in hostels can really be affordable, depending on where all you want to go and how fast you want to move. If you're under 26, get the int'l student pass for tons of discounts.