I learned English when I was 12-14. I got to the point where I could converse in it in roughly 9 months between 13 and 14, after doing a 2x a week class with roughly 12 people. Yes, age is a huge factor, but the class was a part of a school that had multiple concurrent tracks, and ours was doing better than others. Age groups were all mixed and I was the youngest there. The keys to success for me were:
1. Teacher who didn't waste time. We plowed through the course material at a pace of roughly two chapters per lesson. This was double the speed of other tracks.
2. Teacher who wasn't a native English speaker. This was huge. A native speaker of English, even a professional teacher, can't usually explain to you things like the difference between past perfect and present perfect tense. Or how conjugation of pronouns works. Or the rules and exceptions of conjugating verbs in different tenses. She was able to explain this because she had to learn it in a structured way.
3. English is a very structured language. Unlike Russian (my first language), it discourages run-on sentences. It also has a specific order of verbs and nouns. It also has a pretty simple system of taking the same sentence through all nine tenses with mostly modifier verbs (be and have). This all maps really neatly into handy charts that are very quick to memorize. By contrast in Russian you have three tenses, so the difference between "I am walking" and "I walk" is up to the reader to discern.
4. English is simpler than Russian when it comes to conjugation. There is no conjugating verbs, adjectives, or adverbs by gender. The only conjugation you do is by tense. "Exception" verbs suck (be, am, was, will/shall). But aside from the most common ones (be, have, go), they fall into one of several patterns(think/thought, bring/brought, ring/rung). Less conjugation is better, and since English requires complete sentences (you don't generally see sentences like "gone" and have to infer who just left, he or she, etc.) no additional information is conveyed by conjugation. Can you tell I hate conjugation? Basically going from Russian to English felt sort of like going from Python to Basic: you have a lot fewer paradigms to worry about, while already being familiar with the paradigms Basic uses.
5. Lots of memorization of words. Once you figure out how to say "Today after work I am going to get dinner with friends" you can easily substitute drinks for dinner, date for friends, school for work, etc. So I made my goal learning the structure of the language and learning enough words to make substitutions. Once I conceptually knew how to use all nine tenses, the rest was simple memorization and usage.
6. Lots of conversations and not being afraid of my bad accent. You know what's great about talking to other students? They don't give a shit that your accent sucks. Native speakers, especially ones outside the classroom might be nice about it, but you are always keenly aware that you don't sound like them.
7. Finally, after I was able to hold conversations in English, emersion helped. Side note: try not to move your kids to a completely new country and send them straight to high school a few months later. It's brutal.
On the other hand, I have failed to learn any other languages since. Part of it is lack of time and motivation since I don't have a specific need for them. Part is that I am in fact older. I am about to take up Japanese and after that maybe get back to French. To this day I have failed to teach any of my past or present partners Russian.