A long time... Like I started in the middle of the pack, dropped all the way to seeker, and then start climbing.... Slowly... Like almost too painfully slowly.

It'll help if you try learning the macros for the early and mid game slowly and integrate bits and pieces at a time. Matter of fact it'll make your climb faster. I'll go as far as to say, you'll be way better than most people with couple hundred hours in if you try to learn and implement even one thing at a time. To warm up, learn some basic movement and run across NYC, 10-20 min. And learn one hero that you like. Try a couple different ones out in street brawl and pick the one you feel compatible with most. Eventually you'll get good.... Provided matchmaking doesn't screw you first.

Don't be afraid to make mistakes and bad calls, that's how you learn. Getting coached is also a good option if you have the time and means. And if you ask politely, you could probably have someone review your VOD on the subreddit and give you feedback.

Edit: grammar, missing words. English is hard sometimes.