The details of the calculation are a long and complicated subject. But essentially, it's 5% interest on the amount you underpaid at each of the quarterly due dates.
If you don't pay the penalty with your tax return, then the IRS will send you a bill. That's really the easiest way.
However, there are several different ways of accounting for when your withholding was received and when your tax liability was incurred. The IRS uses the basic method of assuming that all your withholding and tax liability was divided equally among the four quarters.
You may be able to get a lower penalty by using an alternative calculation, but you have to show your work to the IRS. If you had more withholding in the early part of the year, then you can enter into TurboTax exactly when it was withheld, and possibly reduce your penalty. Similarly, if you had lots of income late in the year, then you can show that you didn't need to pay earlier in the year, and reduce your penalty.
Side note: stop using the phrase "I neglected to..." This has a specific legal meaning, that you didn't care enough about your tax obligations to do it correctly. Don't admit to neglect, when no one has accused you of it. You simply didn't pay your quarterly tax. That's correct and sufficient, and all you need to say.
