First You must take the backup all your data.then disable the security suites such as antivirus or firewall whatever installed on your Computer and in Galaxy Y
Enable the USB Debugging on your Galaxy Y device through this path – “Settings > Applications > Development > USB debugging”. Remember to check the USB Debugging option at the end.Also tick mark and enable Settings->Security-> Unknown sources.
How to Root Samsung Galaxy Y GT-S5360 on Android 2.3.6 Gingerbread OS
Step 1. first Download the working Root Package update.zip file from here in to your PC.
Step 2. Connect Galaxy Y to the Computer via USB data cable and copy the downloaded update.zip file to the root of the Phone SD card storage.then remove your mobile from pc.
Step 3. Now turn off the device. Again press and hold Volume up + Home buttons together and Power On the device simultaneously till you see the stock recovery mode in the blue screen.
Step 4 . Once you entered into stock recovery mode select ‘install zip from SD card’ and then select ‘choose zip from SD card’ to browse the SD card and select update.zip file to flash it on your device. For confirmation you need to select ‘Yes’.
Step 5. The whole process may take around 5 minutes. Wait till it finishes without disturbing it.
Step 6. When it finish flashing the Root package, you need to select the ‘+++Go Back+++’ option to return to the main menu and select ‘reboot system now’ to restart your Samsung Galaxy Y S5360.
Step 7. The device will be loaded into Android OS there you can see Super SU application in the apps list. If u want to install third party BusyBox apk on your device download it from here.
Warning: Rooting will voids the warranty. Moreover we are not responsible if your device is damaged or bricked.