The first question you have to ask yourself: what kind of maps do you want to make? For you personally? For a game? A book? What style? Informative? Artistic?
Only then can you start to look for the right tools.

For starters, I can only point you to the tutorial section of this great forum. Look around, try a few things and ask if you get stuck.

But the most "beginner easy" way to start mapping is the real old-school version: take out a pen and paper and start doodling!