I masked off the sneakers with blue painter's tape, composed my ideas in Photoshop... and started!
I painted just the areas showing art with 2 coats of matte black gesso, leaving the stitching white. I cut circles of painter's tape to cover the round converse seals.
The inside-facing sides have the TARDIS exterior blue(s) - one sneaker with the "old TARDIS" blue, the other with the new blue. 
After it was dry, I peeled off the masking tape on the seals.
Next I gently sanded the converse round seals (to make the paint stick better, and to conceal the printed letters and stars), and painted them with 2 coats of white acrylic.
Then I traced the symbols in pencil, and filled them in with micron pens. For sharper details, I used an Xacto. I added blue paint to give it richer, less flat look. On the Gallifrey seal of Rassilon, I added distress marks, highlights and shading.
Next was the harder part - painting the TARDIS. I drew it as big as I dared, yet now I can see I could've managed it smaller after all. I wanted them both to be subtle, with stars and space and wibbly-wobbly stuff.
Using my magnifying lens was essential!
On the spines, I added "POLICE PUBLIC CALL BOX". When it was all dry, I covered them in two light coats of acrylic varnish, and I was finished! Peeled off the paint, used an Xacto to uncover the eyelets.
Not sure how they will wear over time, I have heard a lot of people use fabric paints or markers for this. We'll see what happens!
