Safety First

As you are going to do a risky job follow these safety measures before starting.

Your Smartphone should be fully charged or at least with 60% charged, in order to get ready for rootin. If you try on low battery your Device will crash and hence will get Jammed.
Backup all your Data like Images, Contacts etc before rooting because all files will get removed during rooting of the device.
Close all the background applications, especially antivirus and battery checkup utility.

Before Starting, Enable USB Debugging on your mobile. This can be done as follows Settings > Applications > Development.

Rooting your Samsung Galaxy Y S5360

Download update.zip from the link given at the bottom.
Connect your Device Samsung Galaxy Y S5360 to the computer only via USB.
No Extraction is required. Copy the Zip file to the root of the SD card and remember not to paste in any folder as it would cause an interruption.
Never Unplug your Device Samsung Galaxy Y S5360 while rooting.
Switch off your Smartphone to enter into recovery mode.
Keep pressing The Volume Up Key + Home key + Power Button to enter the recovery mode.
Now, as you are in the recovery mode only Volume up and down would work to select the file. So use those buttons and select Update zip from sd card .
Then choose update.zip.
The rooting will start taking place. It would usually take about 10-15 mins
Once it completes, choose reboot in recovery and you will have rooted Galaxy Y.

LINK