There is a lot of gear that goes into playing soccer. Most of it is very basic and you probably already have most of it in your closet. Shin guards are essential to protect your shins from being kicked, cleats help you grip the turf so you don't slip, and socks keep everything together (and prevent blisters). You'll also need a soccer ball - size 5 is standard for adults, and size 4 is standard for kids under 12.
If you're playing competitively, there are a few other things you'll need to get hold of. A water bottle is essential to stay hydrated during long games or practices, and a first aid kit should be on hand in case anyone gets injured. A pump will help keep your soccer ball inflated to the correct pressure, and extra laces can be handy if yours break during the game. Finally, if it's cold or wet out, consider investing in some thermal underwear to keep yourself warm without sacrificing mobility.