So I've heard that you can be a lumberjack of sorts in Skyrim, and gain money from it, but I'm not understanding how. How would you gain money? Who do you get the money from? I have a wood ax but what trees do you cut down? I've gained firewood from the stumps but that's it, any suggestions?

You can't cut down any trees.

You made firewood from the stumps. That's it for "lumberjacking". And you sell the firewood to Inn Keepers. That's it for "money making".

And no, you can't build a fire with 'firewood", as that would be totally silly which is why Bethesda didn't add that feature.

Enjoy.

If you sell the cut wood to the actual owner of the mill he gives you 5 gold for each log. You can also pick crops for farmers and they give you the same for each crop picked