How do I activate my new iPhone with old phone number

You will need to move your SIM card from the old phone to the new one. Or, you can contact your carrier to activate the new phone.

~Lyssa

The answer depends completely on how you purchased the iPhone.

I have had thirteen different iPhones with the same telephone number and cellular carrier. Each time I purchased a new iPhone, I specified this at the time of ordering. The transition was very simple, and did not even require moving the SIM card.