How would I sue a telecommunications company that has a headquaters in a different state for failing to perform?

It does not matter where their headquarter is. If the company is doing business in Maryland, it has a resident agent for service of process. You could find the agent at http://www.dat.state.md.us, file a lawsuit and serve the agent in person or by certified mail. Suing telecommunication company in a State court may be difficult because of variety of so-called preemption issues, however.