You can download The Sims for free using the Google Play market. You have a Free to Play version and a paid one named The Sims 3. The first version allows you to play the game using all the resources available but for certain operations and assets you will need to use real money to buy them. The second version is a one time payment and afterward you will have full access to all the content the game offers.
In order to play the free version, navigate using Play Store found on your phone's application list and search for "the Sims". Accept the installation and you are ready to go.