It depends, there is no exact answer to this question. People who are willing to learn and work hard start getting success after 6 months. Others keep struggling for years.
One major draw back of working online at home is that nobody is going to tell you that this is wrong, this is right, you are not working these days, learn these things etc.
People who are not willing to learn or doing there own research find it difficult to succeed here, although everything is available in both free and paid version but its a choice.
Commonly it takes more then 1 year to see results