Depending how permanent you want your project, try the following options (in order of cost):
1. Ceramic markers/paint to decorate your mug, then bake as per instructions, or use the varnish to seal your project for dishwasher proof.
2. Vinyl - cheap vinyl is intended for indoor use, and the adhesive is meant for removable projects. There are other grades of vinyl for more permanent applications (but probably won't withstand dishwasher or hot water washing).
See other stronger adhesive vinyl here
See some permanent vinyl here
See varnish options to seal your project here
3. Waterslide/Decal paper is a relatively cheap method of decorating items eg. model trains, candles, plates, guitars
See papers to use with laser or inkjet printers here
4. Heat Transfer material can be used on ANY products that can withstand 160° for approx 15sec. You would need a press (mug, cap, plate or combo) to transfer these materials. Sometimes your household iron can do the trick for small projects.
See many different types of Heat Transfer materials here
5. Sublimation methods allow for more permanent results, but this requires your project (mug, plate, etc) to be treated for sublimation. This can be costly and generally requires specialised equipment (Printer, heat press)
See some options here
As per our T&Cs, we only suggest various options for your creative experimentation - it remains your responsibility to test and find the solutions for your project applications.