step by step rooting guide?

[doodle1]

Hi, I have S3 GT i9300xxella 4.1.2. stock rom. Kids have downloaded lots of apps and I've uninstalled them. I've read only way to really remove left behind bits is to clear dalvik cache by entering recovery mode. Does anyone have a link to a step by step guide how to do this? My phone has slowed down a bit so hopefully this clear out will speed up again. Thank you