It is a difficult question to answer, it can depend on many factors; experience, musical background and even if your goal is to sing in the shower or on the stages of London's West End. Some of you may have heard of the 10,000-hour rule, in which they say that it takes 10,000 hours to become an expert at anything. How long does it take to learn to sing? Exactly ten months and three days. If you think it sounds weird, you're right.
Some people are born with very little vocal ability, while others are naturally gifted singers. But everyone, from the shyest shower singers to the professionals, can always learn more about singing. Going from a basic level to an intermediate level of singing takes six months to a year of constant practice. As with other sports, constant repetition develops muscle memory.
Basketball players run drills at every practice. They run laps to gain endurance and practice all kinds of coordination exercises. For most people, it usually takes three years to tear down all the foundations. That said, when you have all the fundamentals as a singer, you'll be a very good singer.
The voice is one of those instruments in which simply laying the foundations is such a task that most people never get to that point. If you are looking to go beyond the basics and learn to distort the voice, extend the voice from your chest as much as possible, etc. It may take another 2 years of diligent practice to lower that. Tuning and tuning problems can often take a few months to correct;.
From there, finding opportunities to sing like local bands, choirs and open mic nights will make you realize how far you've come in your adult singing lessons. You can learn a lot through weekly singing classes, singing courses or YouTube videos, but you need to continually USE the methods and techniques to get your muscle memory into action. You may not always utter words exactly as you would when you are speaking, so learning to sing clearly, without inhibiting your singing voice, is very important in your singing journey. It may be possible to learn to sing on YouTube or in online courses, or sporadic lessons, but deep down, you probably feel that private singing lessons taught by a dedicated professional teacher are a much more reliable way to create the kind of change you're looking for in your singing ability.
After teaching for a few years, I was struck by the number of adult clients who told me how, when they were little, a choir director or family member asked them not to sing. Singing with a one-on-one teacher is certainly not the only way to learn to sing, but it can speed things up a lot for someone to adjust your technique in real time.