When reaching out on social media, think about the person and their position. Are you a mid-level employee trying to contact a CEO? Try reaching out to those who are at a similar level or someone whom you would expect to work with daily if you were to work at the same company.
Consider taking on a website to help brand yourself. You can use it as a way to showcase testimonials of your work and provide a portfolio of work. Make it into something that helps a hiring manager see who you are and all that you can do at a quick glance.
Does your work involve a visual aspect? Try looking into Instagram and Pinterest as ways to connect with like-minded individuals and show off some of your work. Facebook and Twitter also good sources to connect with industry professionals.