Your understanding of step and stamp (or AmE, "stomp") is correct. You could probably live your life with just those two verbs.
"Trample" and "tread" aren't very common words. "Trample" brings to mind stepping through a flower bed or similarly causing damage. "Tread" just means to step and is commonly found in set phrases like "where angels fear to tread" or the American colonial warning "Don't tread on me."
- For Teachers