Good news: you have several options and one of them is much simpler than quarterly estimates. Let me break it down.
Option 1: Quarterly estimated payments (Form 1040-ES). You would calculate the tax owed on your combined income (W-2 plus 1099), subtract what your employer withholds, and pay the difference in four quarterly installments (April 15, June 15, September 15, and January 15 of the following year). The payments cover both income tax and self-employment tax on the 1099 income.
Option 2: Increase W-4 withholding. This is what I recommend for most people in your situation. You can submit a new W-4 to your employer requesting additional withholding. Under Step 4(c) of the current W-4, you can specify an extra dollar amount to withhold per paycheck. If you estimate that you owe about $6,000–$7,000 in additional tax on the 1099 income, you could have an extra $250–$280 withheld per biweekly paycheck. No quarterly estimates needed.
The advantage of Option 2 is that W-4 withholding is treated as paid evenly throughout the year regardless of when it is actually withheld. Quarterly estimates, by contrast, must be paid on time or you face underpayment penalties for each quarter.