Never underestimate the power of social media marketing! Get your business Facebook and Twitter pages up and running and use them as frequently as you can. Twitter can be particularly good for building contacts and really getting your name around (I'm a jewellery designer and silversmith -self taught- and am followed by, and have conversations potentially leading somewhere, TV presenters, magazine editors, management of retail jewellers, galleries and even had a fashion designer from New York stumble across me!), along with potential clients. Facebook moreso for reaching potential clients in your local area.
Link the two to your website and promote that way too.
Photos will be particularly important for you and videos will be a good way to show your work aswell, both can be shared on social media and Facebook is perfect for this as videos and tutorials really do do the rounds.
I'd imagine blogging can be pretty good for your industry, to show what you do, events you've done peoples make up for, tutorials and comments on the make up you use. Again, link these in to your social media accounts.
For your industry, I would also be targeting (liking,following, subscribing to and trying to forge a connection) business pages such as bridal stores and general wedding supplies, event hire stuff etc maybe some beauty therapists and hair dressers who don't do make up (know a mobile hairdresser who picked up a make up artist this way who she promotes and works with for special occasions and shows).
Be creative with your business cards, there are different ways to do this. Mine are tactile with the background being gorgeously soft and smooth, like velvety skin, with metallic slightly glossy feeling logo. It remind me of when you fiddle with your pendant and feel the metal against your skin. No idea if it works but was worth a shot for a little tempting memory jogger! You could try something like a photo of a made up face with the lips actually done in a glossy finish etc Something that stands out?
Maybe offer a referral discount at times, and/or offer night out/special event group make up offerings? Particularly in the run up to Christmas, I've seen that work quite well.
Good luck with your new venture, and well done on setting up your own business, it's scary but fun and a fab confidence booster :)