What is the secret to the moon door next to the weeping waterfall in Fez?

Solution 1:

The door can be opened using its inscription as a cipher.

Solution:

That door is only illuminated at night, but you can enter the code any time of day: ← LT ← → RT ↓ ↑ LT. This code is different from that of the nearby pillar.

Solution 2:

A translation guide from the Fez wiki states the following:

Read in normal vertical orientation, however, the symbols translate thusly:

Use the above cypher when reading rune sequences from TOP to BOTTOM. You must stand under the tablet with runes, or under a set of runes on a wall, and tap the button combinations on the controller with less than a second of time in between for the code to work. You will get the Cryptographer Achievement the first time you input a code correctly.