I can remember the mnemonic our teacher used when it was first introduced to us in primary school.
"Less than" is "kleiner als" in German, "more than" is "größer als".
"<" looks like a part of a "k" => "|<leiner als"
so ">" is the opposite.
That's how I remembered them

, but once you work with them more, you automatically use them correctly.
If you actually think about the shape of the signs, it's self explanatory

(cf. NuclearSilo's explanation

)
Same in Dutch: |<leiner dan. I've learned it that way.