The kinds of decks you can build with the basic cards are not so very different from the kinds of decks you might draft in arena, in that you'll be unlikely to have game-winning combos so it's all about fundamentals, which in Hearthstone right now are tempo and value, probably in that order. So look up some recommendations for decks using only the basic cards, then play some ladder games against people who (at least at first) are likely to be in a similar situation to you.
Watching pro players streaming is a good way to improve, although you have to be lucky enough to choose somebody who's explaining things at your level.
For arena, do you know about Heartharena? It's a website that will take you all the way through the process of a draft, making recommendations and often explaining them, finishing with an overview of your deck and how they expect it to play. I still find it extremely useful, even if I don't use it all that often.