New versions are released from time to time. Depending on the platform, upgrading is usually pretty easy, but there are some concerns to be aware of.
If you've installed from Google Play, upgrading is handled automatically by Google Play on your device.
However, if you installed the APK downloaded from ppsspp.org, it will not automatically update, so you have to manually download an install a new APK to upgrade.
If you want to install by another method than before, or downgrade to an older version, you need to uninstall first (in which case you should make sure to backup your save games), since the digital signatures are not compatible.
If you've installed PPSSPP by downloading the zip file and unzipped it somewhere, you have two paths:
Either will work, matter of taste.
If you've been using the installer before and are using the installer again, it should just work to install the new version on top of the old one.
Both on Android and PC, PPSSPP Gold can be installed side by side with the regular PPSSPP. If you make them share PSP (memstick) directories though and keep different version of them, they may have problems sharing save states due to the above-mentioned backwards compatibility issue.