[Alcuin]

Aragorn had entered Moria from the east, through the Great Gates in Dimrill Dale. When he did this, we are not told. I have read some speculation that he might have lost a companion, such as another Ranger, in Moria. In any event, when the Company of the Ring fled after Gandalf fell into the abyss, there was a company of orcs guarding the entrance. We do not know if this was typical after the orcs re-established themselves following the Battle of Azanulbizar: perhaps they were watching for travelers through the Mines (i.e., the Company of the Ring), or perhaps it was normal procedure. Somehow, Aragorn got in, alone or (more likely) with others; but he escaped only with difficulty, and the memory of the experience was so black, he was willing to attempt crossing the Redhorn Pass in the dead of winter knowing that his transit was probably being watched.

Gandalf said that only he had passed completely through the Mines. Since he exited through the Doors of Durin, he must also have entered from Dimrill Dale. And since he alone had transited the Mines, Aragorn cannot have accompanied him, giving us the additional information that Aragorn also entered and left through Dimrill Dale.

I cannot recall reading in Silmarillion, Unfinished Tales, Letters, History of Middle-earth, or Reader’s Companion of any further exposition of Aragorn’s (mis)adventures in Moria. If anyone is aware of anything else Tolkien wrote about this, please post it!

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added: After Boromir carped about opening the Doors of Durin to enter Moria, Gandalf told him he had entered from the east.