You could make the monogram any number of ways. If you are truly talented you could free hand Calligraphy, or use a stencil like I did. You would have guessed I bought it at Anthropolgie.
All you need is a ceramic mug, I bought mine at the Dollar store, and a Gold (it has to be a Sharpie).
After you've finished your design, you bake it in a Preheated 350F oven for 30 minutes. Turn off the oven and allow the mugs to cool completely before wrapping or using them.
Here are similar ideas for your viewing pleasure to help you inspire you, like this one, or this one , if you love succulents, you could turn a mug into a pretty planter. The possibilities are endless. Here is one more idea for you, take a look at the DIY Watercolor mug I fashioned not too long ago.