I justwant to provide some clarity here since you're a new business owner.
You don't "file" a quarterly tax return. You "pay" quarterly taxes.
To pay the IRS online I find it simplest to do so at www.irs.gov/payments. Just remember to print your receipt and file it with your business records so you will have it at tax filing time next year.
If your state taxes personal income, you will need to pay your state separately. How you pay your state, depends on the state. Not all states offer the ability to pay quarterly taxes online. So if your state does tax personal income you'll need to contact your state taxing authority for how to pay, or you can check their website.