You need to mail it - You should have seen a page with instructions on where to mail as I just did my state. Or u can check your state Revenue Department online for mailing address.
If you owe money to state AND extended federal you can also extend your state to July 15th without incurring interest. If you didn't extend federal then you should mail your payment in by tomorrow. That was my understanding from my state.
If it's large payment you should contact them on payment plans too.