What you need:
Cheap white mug
Dry Erase Marker
Black Sharpie Marker
Locate a plain white mug. I got mine at the dollar store. I found a cool angular one that perfectly fit the delta shield shape.
Find the combadge of your liking online. Print it out. I used the Voyager-era combadge. Cut around the edges.
Stick your combadge on the side of the mug with some double-sided tape. Trace around your template with a Dry Erase Marker. This will make your design mistake-proof. If you mess up, just wipe away with a paper towel and start over.
Go over your design with a Sharpie for a lasting effect.
Handwrite your favorite quote. I chose Janeway's "Coffee. Black." But, you could easily go with Picard's "Earl Grey. Hot."
Bake your mug in the oven for 30 minutes at 350 degrees. This will ensure the design stays on without smudging or scratching off. Remember, to use an oven mitt when taking it out and do not touch the design until it fully cools off. You might want to avoid putting it in the dishwasher just to be safe! Hand wash only.