Maybe you know this, but:
The important distinction to remember is that 下げる is transitive (it takes an object, the thing that is being lowered by the subject), while 下がる is intransitive (it takes no object, the thing being lowered is the subject).
So, for example 音量を下げる means that somebody lowers the volume, while 音量が下がる means that the volume lowers. (Often the particle used is a telltale sign of an intransitive vs a transitive verb)
As for your actual question of how I remember which one is which: for these two I actually use the mnemonic that came with the vocab… for whatever reason you’re lowering a sage (さげ), so the げ one is transitive!
There are general rules for these transitive/intransitive pairs (there are a lot of them!) as well, but I’m not sure they’re 100% and I also don’t know them that well!