Most of the time a firmware upgrade can be done with an executable file. In case of your Lite-On drive for example you can download an exe-file from the Lite-On website. It's then very easy to upgrade the firmware of your recorder simply by starting the file, selecting your drive, pressing flash and rebooting your system. That's normally all there is to it.
Sometimes though, firmwares will be available in binary versions only which requires additional (flash) software in order to load this file and flash it to your drive. This loader software should be available on the website of your drive manufacturer. Last but not least you can also find firmware that has to be used in DOS and cannot be used via Windows. These are quite rare I believe.
The benefit of upgrading the firmware of your drive is overall better read/write performance. Firmware upgrades will improve media compatibility and sometimes they can even add totally new features such as Mount Rainier support. You can the website of your drive manufacturer to check of they've released a changelog on what's new in a particular firmware version. Lite-On's changelogs are almost always the same (match more media) but out Lite-On forum has more information on what has changed exactly in a certain version.
Lite-On recorders can sometimes also be flashed with the firmware of a different model. For example you could force a firmware flash from a 48x drive to a 40x drive, making the 40x drive into that 48x drive (and thus increasing its write speed). More information on â€˜overclockingâ€™ Lite-On drives can be found in the Lite-On forum.
I general would say that the best firmware for a drive is simply the latest version. Hope this answers your questions!