For all those crafty Whovians out there!
I have a video tutorial for this project, which is very similar to the one below this step, but the tutorial below actually has more detail.
Place paper Tardis on mug and tape around it so you have a nice area to later fill in with a sharpie. This part may look complicated, but you simply cut little square notches in the tape to fit around the tiny square pieces of the Tardis.
Otherwise, you can try cuting out the Tardis from contact paper or a large piece of tape, stick the outline on it and do it that way.
OR, just use thicker paper, use tape to attach the Tardis, and hold the paper down as your outline the Tardis and then fill in the Tardis.
Press the tape down firmly. IT IS OK if the marker does seep through the edges because as long as you have a dry-erase marker or nail polish remover you can fix any errors!
Alright, peel off the tape and tidy up the edges by drawing ON the errors with a dry-erase marker and then rubbing off the dry-erase markings. DO NOT rub the dry-erase marking off toward the inside of the Tardis or it will rub off part of the Tardis and you'll have to color in that bit again.
Now is the free handed part, which, if you want to use a piece of thick paper to help draw straight lines on the Tardis you can, I do not recommend using tape on the parts you already colored though. First, I added the window lines, drew some little lines to look like writing, and added a bar for the "police box" sign.
(Use a fine-tip sharpie for this.)
Final step is adding a cute addition to the inside of the cup. I had already watched a tutorial for sharpie mugs and a the person added a heart to the bottom. I figured that I could do the same, except add TWO hearts because The Doctor has two hearts. I folded small circular price marker stickers in half, cut out hearts, taped the outline to the bottom of the cup, and colored in with marker.