Just how did Gollum escape Mordor?

[Aganzir]

"He's been here before. Came out of Lugbúrz the first time, years ago, and we had word from High Up to let him pass."

-Shagrat to Gorbag in the Choices of Master Samwise

I've always taken it that he was set loose. Besides, it just couldn't be that easy to escape from Mordor.

I think I've read something about how he got on the Fellowship's tracks but don't remember now. He was first taken to Mirkwood and then to Dol Guldur, right? I have no idea how he ended up in Moria then.