Check out this great piece in Inside Higher Ed: "Grad Student: You Are Your Own Spokesperson"
Here are a couple of excerpts:
Want to effectively represent yourself? Plan accordingly. Develop communications skills that work for larger audiences and think about ways to connect with individuals or small groups. Tend to your social media identity and compose a few different elevator pitches. Leverage the contacts you do have and plan to reach out to contacts you’d like to have. Remember that when you find your dream job, you’ll probably have to talk your way into it.
The bad news is that if you’ve been in graduate school for a while, chances are your communication skills aren’t up to snuff. You might have developed public-speaking and self-presentation habits that won’t work beyond academe. These habits might also be hurting your chances for an academic career.