Of course the best place to get started is the Games Workshop website on getting started.  There you will find lots of information on where to find the products, how to assemble and paint the models, and a couple of videos on gaming.  

After that, the Warhammer Community website is the place to go. Part of Games Workshop, the Community website has daily news about games and has several sub-website dedicated to getting started in Age of Sigmar or Warhammer 40,000.

For Age of Sigmar, you will also want to check out the free downloadable core rules and FAQs/Erratas.

​For Warhammer 40,000, there are likewise free downloadable core rules and FAQs/Erratas.

Finally, if you want step by step guides on how to paint your miniatures, download the free Citadel Paint App or search for "how paint gw [your model]" on YouTube.  
A new edition of Age of Sigmar brings many changes to the rules and possibilities to play.  Fortunately, Games Workshop has produced a series of short tutorial videos - together with Becca Scott of Geeks & Sundry - to explain all aspects of how the game is played.  They are available online, but we provided links below to help you find them faster.
Games Workshop provides a free Warscroll Builder that makes it easier to create army lists, and it also provides the outstanding WH AoS App that include a more robust (but not free) army builder called Azyr. The WH AoS App allows you to purchase electronic copies of all Age of Sigmar battle tomes, novels, and rules - plus it has the war scrolls in electronic format for all units in the game.
Regrettably, Games Workshop has not produced similar "how to play" tutorials for Warhammer 40,000.  But below are some short video tutorials from outside sources.
Games Workshop provides a free Combat Roster that makes it easier to create army lists using power levels.  There will be a points-based army builder released by Games Workshop in the future, but for now many people use the free third-party Battlescribe App to create points-based lists.