maasthrict to madrid

First guess: train to Eindhoven, bus to Eindhoven airport, then Ryanair to Madrid.

It all depends on when you want to travel (Ryanair don't have daily flights), how much checked baggage you have etc.

For more flights have a look at Vueling as well.

It takes a lot longer but may be cheaper by bus with Eurolines.

Not sure if it was a typo, but since it's the same in the title and your post: it's MaastricHt (also to help you find the best connection).

I confess that I never understand what people mean when they ask about "the best and cost effective way" of getting from A to B.

"Best" can mean a lot of different things to different people: for example, fastest, slowest, most scenic, cheapest, most comfortable...and so on.

"Cost effective" when it´s applied to travel? I have no idea what it means.