First you need to download all the files necessary for the rooting procedure from the below given links,
Samsung USB Drivers
ODIN v3.07
Touch Recovery and Non Touch Recovery (CWM Recovery File)
Root Package
Please download all the above given files to your PC desktop.
2.Once the files are downloaded you need to copy the "root.zip" file to your Galaxy Ace 3 sdcard root folder.
3.Now install Samsung USB drivers on your PC
4.Once you have installed the drivers enable "USB debugging mode" on your Galaxy Ace 3 and switch it off.
5.Now enter it in "Download Mode".
6.To enter Samsung Galaxy Ace 3 in "Download Mode" press and hold "Home"+"Volume Down" and press "Power" buttons until you see a warning screen like the one given below,