Do you want it to look like clear glass, or frosted? I am not too handy with fondant but I know that if you wet it, it will turn shiny. Maybe use a spray bottle with a very fine mist?
you can buy an edible varnish, or hold the mug over boiling water not to long just a few swipes and it will make it shine, or is you have a clothing steamer
I watched the CakeBoss and he used a steamer to make the fondant shiney. I used a garment steamer and it worked. Make sure you don't put your buttercream decorations on until you finish or if you do just be careful not to steam too much. the buttercream will melt.
Yes, definately the garment steamer is the way to go. It works like a charm but don't oversteam because your fondant and decorations will start to melt and droop!!! Another option if you don't have a steamer is to mix half corn syrup with half vodka (mix until corn syrup is fully dissolved!) and paint on with a brush. I have used this technique a few times and it really leaves a super-shiny finish even after it has fully dried. Good luck!!