In order to become a professional make up artist, what you have to do firstly is creating portfolios. Portfolios in here mean the professional photographs for your work. Employers mostly want to know about your ability right? In order to know about that then you have to make the best portfolio to catch their attention first.
The second is join many fashion and beauty events so you can meet many people there and create networking. Who knows some of that are fashion designers that might want to hire you for the next show?
The third things are by submitting your portfolios not just for agency but also for magazines. If your portfolios are great enough then the magazine would write a review about it especially in their beauty column. Once you are in magazine then broader your chance to be known and get more networks from it.