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.

If they are doing business in Maryland, they can generally be sued in Maryland. If the amount in controversy is large enough, you may want to consider suing them in federal court.