Independent contractor

Are you referring to making quarterly estimated tax payments for 2018?  If so, the date for making the final quarterly payment for 2018 has long passed.  That date would have been January 15, 2019.  

If you WERE required to make quarterly payment for 2018, please make a payment as soon as possible.   You'll be penalized for late payment and interest.

I'm linking you to the IRS publication that explains making estimated tax payments, due dates, how to make payments, and worksheets to help you calculate your estimated tax payments.

For 2019, you "should" have made 3 quarterly estimated tax payments for your business.   Again, you need to make payment as soon as possible.  Underpayment penalties and interest can be significant.

 https://www.irs.gov/pub/irs-pdf/f1040es.pdf

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The wording of things can be (and usually is) very misleading to a first timer. One does not "file" quarterly taxes. You "pay" quarterly taxes. Then you "file" a tax return once a year.

you can pay your federal quarterly taxes to the IRS at http://www.irs.gov/payments.  If your state also taxes personal income, then you'll need to pay quarterly taxes to your state too. Your state payments would be separate from your federal payments to the IRS. How you pay your state taxes depends on the state, as not all states have the ability to pay online. So check with your state's department of revenue or department of taxation website.

Quarterly tax payment date deadlines for 2019 taxes are:

Probably the easiest way is to pay online, using the Electronic Federal Tax Payment System that's available here:

https://www.eftps.gov/eftps/direct/EftpsHome.page

At this site you can schedule future payments as well as any payments that you want to make currently. 

The US tax system is a "pay as you go" system and most folks "pay as they go" by having taxes withheld from their paychecks.  If you have significant income that's not subject to withholding, e.g., independent contractor income, you may have to pay "estimated taxes" directly to the treasury.   Generally these taxes are due more or less quarterly around 4/15, 6/15, 9/15 and 1/15 of the following year.  I emphasized the word "may" because it's not exactly a hard and fast rule.  It's perfectly OK to owe the government a lot of money when you send in your income tax return, but if you're "underpaid" - a piece of tax jargon with a definite meaning - then you could be subject to underpayment penalties.

Look at the "General Rule" at the site Kat has provided and the "Special Rules" and you may find out you don't really need to make an estimated tax payment, depending on your personal situation.