Check the stickys at the top of rooting, ROM and hacks part of this forum which will have links to all the rooting info you need for this phone. You could also simply Google "how to root galaxy S3 I535" (if that's your model) and you'll find a plethora of results, many of which will bring you right back here.
But just a word of caution! Be very thorough and do tons of research before rooting, especially the section involving the bootlocker. The process of unlocking this on the newest galaxy devices is nothing to take lightly. Samsung/Verizon decided that they want to discourage people from modifying their devices, so the workaround for this is should be followed very closely. I don't say this to scare you, but rather encourage you to get all the info you can. Whatch videos, print out instructions, ask questions, do research, and you should be fine. Just take your time and follow instructions.
Also, if you've received the 4.3 update you may want to wait awhile because its rumored that this update has added new security to discourage rooting. Developers will quickly find another workaround for this should it be true. You can check which firmware you have by looking under settings/about phone/Android version. Most likely you'll see that you have 4.1.2 which is safe to root via the methods I mentioned.
Remember, information is power. Just be careful with it.
Good luck, and have fun. Once you do it you'll realize it wasn't so hard and you'll feel a little more experienced and empowered.
Let us know how you make out
