When traveling abroad, there can be so many options on how to get where you want to go. During my six month study abroad, I always liked to weigh my options. This is what I found:
Bus: Flixbus, a German bus company, is generally the cheapest option to get from point A to point B. You can take 13-hour overnight buses, as I did for my trip to Berlin, which save you what we travel enthusiasts usually call a "travel day". Or, you could be taking a 2 hour Flixbus to a closeby airport if that airport had cheaper flights than the local airport. Over my six months, my Flixbus adventures ranged from 20 euros for a roundtrip to Berlin, Germany from Strasbourg, France to 60 euro roundtrips to Brussels, Belgium. It was reliable 7/10 times, and generally pretty clean. However, one does have to keep in mind that 50 people sitting on a bus for 12 hours is not always a pretty sight....or smell....
Train: The trains in Europe are super speedy, waaaay faster than the Flixbus. However, I was dissappointed at the prices. They were most likely way more expensive than I imagined they would be. Of course, the more flexible with timing you are the cheaper you can find. I also registered for a student pass with my student visa, so if you are there on a long-term stay this is a possibility to cut off some euros. Trains that I took were always very clean and nice, generally quiet, and super easy. A tip: Download the OuiGo app if traveling in France—there is usually a very cheap one-time-a-day ticket to France from other locations that will only be about 25 euros, compared to 40-80 euros.
Plane: If you don't have much time in a place, I would say that traveling by plane is the way to go. If you're on a budget, you can look for cheap flights on kiwi.com and compare different places, times, and airlines. The "cheap" ones are EasyJet, RyanAir, Wiz, and a few others. Be very careful about the carry-on+personal item fine print for these airlines, because you may end up having to pay to check a bag if you make a mistake. The good thing about flying in Europe is that it's not like flying state to state in America—you can get to another country for as low as 40 euros if you're lucky. A lot of airlines have deals to places for specific days. For instance my flight on RyanAir from Strasbourg to Mykonos was 70 euros roundtrip as long as you go from a Monday to a Monday or a Friday to a Monday.
All in all, it takes some research. There will always be different options and what's best is based on your time, your finances, and your preferences!