The surname is changed when you sign the register/certificate at the wedding service. As soon as you have done this, your new surname will be legally yours.
You will then need to use the Marriage Certificate as proof to change passport, credit cards etc etc
My married surname is my maiden name hyphernated with my husband's surname. I Just decided that was the name I wanted and that's the way it is on all legal documents. When I had to renew my pass port I was told I could choose which name I wanted as your maiden name is always legally yours. So my pass port is my hyphernated surname.