Duels of the Planeswalkers could be a good way to learn i guess, i never did though, and generally dislike digital magic. MTGO is alright when it doesn't crash, and Arena seems promising, Duels games were v dull the times i have tried. I've seen people learn quickly jumping into weeknight paper drafts and getting trashed, but essentially getting tutored by the friendly nerds at the shop. YMMV depending on your local scene of course, but imo getting sunk in limited events is likely the quickest way to learn the core concepts of the game; how to value cards, how to build decks, how to play well. Draft can be brutal though, especially after the set's been out a few weeks and you're up against people who understand what the key archetypes are, and can easily pick the best cards pack to pack while you fumble around. If drafting for the first time prob do a pre-release, or go to a casual draft in the first week of a release.
Your LGS will usually have learn 2 magic events occasionally too where they supply casual decks.