There's two ways to sew ballet shoes: straight across the foot and in the X-shape. Since this tutorial has so many photos, I'll break it up into two parts. This will be the X-shape sewing tutorial (since I just got a new pair of shos that I want to sew!). This method will also work for sewing pointe shoe ribbons up until step 2 (there's a special photo for pointe shoes), not elastics. Sewing pointe shoe elastics (I don't use them, so I wouldn't really know) should be somewhat like sewing the ballet shoe elastic straight across the foot, so see my next tutorial for that (or maybe ask your teacher - I'm not really sure what I'm talking about here). Update: here's the elastic straight-across tutorial - Part 2.
For the X-shape, you're trying to make your shoe look like this (I'm too lazy to actually sew my shoes right now, so web image):
Ignore steps 1 and 2 if your elastic is already pre-sewn to the back of the shoe (half of the work is already done for you), so it looks like this:
|Unsewn new shoe. <3|
|See the back of the insole where my finger's pointing?|
|Pointe shoe - see how the ribbon is tucked in the corner at that angle?|
|Pull the elastic down to your arch.|
|Marks on the instep - make sure you're not sewing your elastic|
on the outside so that it ends up looking like this picture!
|See how the elastic is on the inside of the shoe? I might sew it across another time|
if I want it to hold better - I just resewed these shoes for performance, so I did it quick.