What is the most economical way to fly from Frankfurt to Budapest or from Prague to Frankfurt?

Thank you so much.

your best option is to search using www.kayak.com

For budget airlines in Europe try either whichbudget.com or skyscanner.com.

You could also check the trains. Frankfurt to Budapest is a long trip at about 10-11 hours but also is under EUR100. Prague back to Frankfurt is only a 6 hour trip but the EUR40 or so fare may make it attractive to you taking into account time to/from airports and post check in down time.

I don't thin Kayak covers budget European airlines.

I usually use whichbudget to find routes (but they are often marked as nonstop when they aren't), or I use www.opodo.fr which is something like Kayak in Europe but it includes budget airlines like Vueling, Germanwings, Airberlin, etc. as well as the big ones. So you don't have to go search each website for the fares like when using whichbudget. Opodo even includes Ryanair, Easyjet, etc. I believe that is like Skyscanner, so both of those are easier to use as they show you the fares (whichbudget shows you one fare, but as I said, they are often wrong on routes).

If you need another language, they also have www.opodo.co.uk in English but the rates will be in pounds. They have lots of countries, but I think the rates and language go with the country you pick.