Of course, there is no simple answer to this question.
The bad news: You won’t wake up one morning and have perfect ears!
The good news: Every day of ear training practice contributes to your ability: you’ll be continually improving and seeing benefits as long as you’re training.
How long… to do what? From where?
How long it takes to achieve your goal depends primarily on what you want to achieve. Do you want to play by ear when jamming with your band? Do you want to instantly recognise chord types? Is it perfecting your rhythm and ability to keep a beat which motivates you?
The other key factor is where you’re starting from. Whatever the goal, some people will have a good underlying ability already, which just needs to be brought out and defined. Others may find they are building the ability from scratch, which will naturally take longer.
There is a huge variety of ear training a musician might choose to do, and every musician is different. So depending on the details, the answer to this question really might be “two weeks” – or it might be “a lifetime”!
How to plan for fast ear training progress
Rather than ask the question “how long does ear training take” (which can have no satisfying answer!) the best approach is to think in terms of what you want to be able to do in music. Then figure out what kind of ear training will help you build that ability.
Set concrete goals and then (this is key) break them down into manageable milestones. For example, if your goal is “I want to play basic chord progressions by ear” you might decide that ear training on chords and chord progressions is what will help you most. Your milestones might be things like: Identify major and minor triads. Identify common chord cadences. Identify progressions using the I, IV and V chords. Then introducing the vi chord and more complex progressions, and so on. Keep the milestones manageable, and the goals meaningful.
Just as with any musical ability, developing your skill will take time. Improving your listening skills through ear training is really a process of training the brain, and that requires some repetition over time to adapt!
Consistency is key: aim to practice every day. To stay motivated, find ways to keep your practice varied and interesting, and connect it to your world of music.
Don’t see it as a one-off sprint! Ear training is a key part of your musicianship, and as long as you are learning music you should be seeking to improve your ears.