You have to install LG PC Suite IV on your computer first. The installer is found on the memory card that came with the phone.
After you have installed LG PC Suite, connect your P500 to the computer (make sure it's not Mass Storage only). After that, it you will have to make it detect your phone. Once it's found, press the Check for updates button for the phone (or a button with a similar meaning). It will then check for updates. Once it detects that the Android 2.3 update is available, it will prompt you and then tell you to install some software updater.
After that, install it and then the software updater will scan your phone and once it has detected that your phone has an update, press the pink Update button. It will warn you that you need to back up because all your data will deleted, but that's optional as the update won't delete any of your data. Then it will start to download the update and then install it (during this time, don't touch your phone). Once it finishes it will prompt that you are complete and you can close the program. After that your phone should be seen rebooting. If not, turn it on yourself.
It will take some time for it to boot so be patient and not do anything to it while it does. Once it finishes booting, you will find your phone with Android 2.3 in it (there will be a setup thing like you did when you first had your phone). After that you're good to go. Next time you turn off and on your phone again, you will notice that the boot time is significantly faster than it was before.