Don't give up. You'll loose. A lot of times. Before you start to get the hang of it and it will become fun.

Abandon all life. Forget that the world exists. It's you and that big screen of yours. Nothing else. Have a potty and a bottle. Order food, do not even think to shower.

Joke aside, you would probably find some good tutorials on youtube.

https://www.youtube.com/results?search_query=darkest+hour+hearts+of+iron+tutorial

What about Europa Universalis 2? I mostly see EU3 and EU4 on Youtube. It is often claimed that the manual is not the best way to learn how to play this game.

Another question: should one start by playing a big power or a small one?

http://www.combatsim.com/memb123/htm/2002/02/eu2-guide/

Pretty decent, i'd say. And in the old games, the big powers are recommended for learning. Small powers should be chosen once you've started to understand the gameplay mechanics (do not forget that despite the appearances, the gameplay is different for each game)

Well, I bought EU 3 in the weekend sale and started to play as Bavaria. I soon found out that playing a small country is totally boring, since you are only sitting in front of your monitor and waiting for something to happen. There is really not much that you can do in this game besides sending out some trader every now and then. Research takes ahes and to rersearch really helpfull technologies will take about 150 years of gametime. The money system is totally randomized as it seems. I wasn`t able to figure out how to get a bigger income.
In a few days I will try a bigger nation, maybe that makes more sense in this game. But I wonder then, why the game is designed this way, so that small countries are totally useless and boring.

I thought that smaller countries would allow you to concentrate on learning your way around most of the game...