While this may sound like a simple enough question, the answer depends on a number of different factors. To give you a straightforward answer, the United States Foreign Language Training service puts an exact number: 828 class hours, or about 36 weeks of intensive study. If you're planning on taking an intensive job where you need to be very advanced in the language, that's a pretty good estimate. Here's a rough estimate based on some other, common goals for the language:
Vacation to Germany (or another German-speaking country)
Roughly: 15 to 30 minutes a day for three weeks
If you're just interested in getting some basics down before a trip, then you can get there pretty quickly. Focus on the topics you'll need the most: saying hello to people, ordering food, checking into your hotel, and so on.
Simple Conversations
Roughly: 30 minutes a day for three months
Want to try making real connections with people? We'd recommend at least a few months of study, though once again you don't need to make a big commitment every day. You might be surprised just how quickly you'll be able to have quick conversations with people.
Move to Germany
Roughly: 9 months of 30-45 minutes a day
For the record, this recommendation is more a starting point, with the idea that once you move to the country you'll be in a new kind of immersion course. If you're regularly practicing for nine months or more, though, you should be able to get a solid grounding in the language.
Start a New Career
Roughly: 2 years of 30-45 minutes a day
If you want to get a job where you're using German, things are of course a bit more serious. While technically you could stick to a daily schedule like the one above, we'd recommend trying more intensive options, like immersion courses, which will help you speed up your progress.
Brain Training
Roughly: however much you want!
Studies have shown that learning a language is great exercise for the brain. If you're learning a language for the cognitive benefits, then there's really no set deadline. Just make sure you're working on it regularly — even for just 10 minutes a day — and after a few weeks you'll hopefully see good progress.