It wasn't a process so much as an accidental by-product of what I was studying. By the time I left high school, I was taking German, Latin, and French. In undergrad, I expanded that to include some Old English, Mandarin Chinese, and Arabic. You can't get around memorization to learn languages.
The reason my memory ended up so nuts is that I was only interested in the nuts and bolts of the language, so I didn't continue on with French when it became about literature, I just picked up a new language instead. After a while, languages become more about things like context clues, but at the beginning and intermediate stages, you have to memorize a lot. Since I wanted to go for linguistic breadth (since I was interested in how languages were related/how features travel), I did the memorization stage of language learning a lot.
So I'd say it's down to consistency and longevity of practice. I used spaced-repetition as my main technique, but it's really down to spending 1+ hour a day for 8 years on memorizing.
You also have to keep up with it, or your memory degrades. It's been a good 10 years, and I don't have nearly the memory I used to.