Do great work, learn business and marketing basics (these days there are lots of great books out there aimed at artists).
Accept even the most simple jobs and do them well, success will build upon itself.
Don't worry about developing a style or a name, just worry about doing your best and keep learning.
Have a good portfolio website and don't get sucked into spending a bunch of time on social media showing your work to your friends.
Investigate what other successful artists with work similar to yours are doing to gain exposure. Build on these ideas to develop your own market.
Have business cards at the ready at all times, and exchange cards even when you think the person you are conversing with is not a potential client. Network building is an important part of any business.
And I'll say it again -- do great work!