The Samsung Galaxy Y S5360 is Young Generation's phone as per Samsung. It doesn't have much in terms of its specifications and that is exactly why there has been no significant updates in its firmware since its release. The best thing you can do is try to find a good stable ROM which looks like ICS. The Version will still remain as 2.3.6 but the ROM will make a lot of changes to the general appearance of the Galaxy Y's User Interface. There are a few useful and stable ROMs for the Galaxy Y and here is a round of some of the most stable ICS like ROMs for the Galaxy Y.
First thing you need to do is Root your Samsung Galaxy Y S5360.
Next follow the same method of flashing a zip file and flash Clockwork Mod Recovery. In case you don't know how to flash a zip file here is quick gist of it.
Download the *****.zip to flash.
No need to extract. Copy the zip file to the root of the SD Card and do not paste it to any folders in the SD Card.
Now switch off your phone
After the phone is switched off, enter into recovery mode. To do this, hold the power, volume up and the home button simultaneously.
Now can navigate through recovery mode only with the volume up and down buttons. Select *****.zip and the root will be applied on your Galaxy Y.
Next thing you need to is just flash is the ICS ROM you want to install. Here are a few ICS ROMs which are stable and also looking like Ice Cream Sandwich.
That's it. Now you have successfully installed an ICS ROM on Samsung Galaxy Y S5360. If you have any doubts or know better ROMs feel free to comment.
Update: This ROM is a bit more difficult to install but it brings Beats Audio to GT S5360. Try out the Bazzr0m ROM which is still in beta from here.