The IRS charges no underpayment penalty if what you paid in by each due date covers the smaller of 90% of this year's tax or 100% of last year's - 110% if last year's AGI was over $150,000 ($75,000 married filing separately) - and last year's return covered twelve months. If this year's tax less withholding comes to under $1,000, no estimated tax is needed at all. The amount is paid in four equal installments: April 15, June 15, September 15 and January 15 (a weekend moves it to Monday; holidays are not counted here).
A payment counts toward the installments due on or after its date. Each one needs the IRS confirmation number (Direct Pay, EFTPS or the IRS account) before it is recorded. The penalty itself is figured on Form 2210; this shows where the year stands against each date.