I reckon, to set the foundation for anything (Martial Arts or anything really) you need about 100 hours of dedicated training (As suggested by the other answers above).
Divide that over any number of weeks and sessions you want, it doesn't all have to be with an instructor, but the 100 hours should be relatively focussed on the art itself, and not the supporting conditioning that goes with it.
For example, doing push ups and squats may be useful in building strength to kick and punch, but in the end if you do lots of push ups, you get better at doing push ups.
Also, learning Martial Arts on your own is a bit like learning to play basket ball on your own, you can get great at getting the ball in the hoop, but add another person in to play with you and suddenly your abilities aren't as good as you think they are.
Probably worth thinking of the 100 hours in context, for example, 100 hours of learning the art will still mean that you need another 100 hours of controlled fighting/sparring, but this still equals zero 'real' fighting, so always best to remember that too. You can replicate reality to a point, but it's never real. I was lucky that I was in my teens and went through that arrogant stage early and didn't get myself into too much trouble. I knew others that did though, and many blackbelts which got completely flattened by people who had never had a days training, but had clocked up many real fights so knew what reality was like.
Note; The idea of '100 hours' is a personal observation based on Malcolm Gladwell's notion of the fact that it takes '10,000 hours to become an expert' that he made famous. From other personal observations I wondered if the pattern was similar for non-expert. It appears to be e.g. a Shotokan Green belt (a foundation grade) would be around 12 months twice per week (100 hours). The effort (in hours) always seems to be more relevant than the duration. Same for other disciplines including sports, playing instruments, even how well people performed at work in certain tasks.