I stepped on my dog’s foot by accident. In situations like these (where the dog is obviously hurt and shows it by crying loudly), what is the first thing to do to make it clear that the injury wasn’t on purpose and that I am not angry with the dog?

This issue has been addressed beautifully in My Dog: The Paradox – The Oatmeal (final panel):

This raises the interesting question of whether dogs always realise that you did the stepping—let alone whether it was intentional.