How would you delete the shoe from this image?

the best way to approach how to do something in photoshop is to ask "What is the least destructive way of doing something". You don't want ever us the eraser tool for something like this because the eraser tool is final, destructive. you want to mask. you can use the quick selection tool and with the refine edge dialog you can polish your selection. Always use masks, dynamic effects and smart objects, this way everything is super editable for you and others.

Another vote for the Pen tool. I would make a Vector Mask for the front shoe:

I used a temporary Levels layer and dragged the shadows way to the right to find where the shadow of the sole ends, to keep the shadow from having a hard edge. Onect the Path is complete, I then hid the Levels.

If you cut the shoe along the bottom of the sole, you could isolate the shoe from the shadow. You could then add a duplicate layer that clips to the shadows, and set its Blending Mode to Multiply, then linking the two layers. You can then drag a copy of these to a background of your choice:

I agree with Davecm.  Use the Pen tool.  You can add anchor points and adjust it to perfectly surround what you want to isolate