No one can play "The Sims 3" demo anymore without internal access to the company's files. The original demo released by EA was made to be played in-browser on their website, and as the site no longer hosts this online demo, it is no longer accessible to the public.
The original demo was a 20-minute teaser for the game and some of its early expansions that presented some of the new features alongside the familiar gameplay elements of the previous games in the series. The demo featured several different ways to play through it, allowing the player to choose from a few archetypal premade characters and go on a few different guided adventures through some of the scenarios made for the main game.
This demo is no longer available due to the nature of the platform that EA chose to release it on. The game itself is still sold at a discounted price due to the age of the game on EA's website. "The Sims 4" is now out, and as such, "The Sims 3" is no longer being added to.
Those who wish to pursue "The Sims 4" can trial a demo of the sim creator on the EA Origin website, and a trial of the full version of the game can be played for 48 hours free on the same website.