An extension only gives you more time to file your tax return. It does not give you additional time to pay your income taxes. So how do you know what to pay if you haven't completed your tax return?
You can use your previous years return as an estimate. If you owed $1000 the previous year, pay as much as possible of that $1000 towards this years return. This will lessen the penalties and interest assessed for any balance paid after the due date.
The next step will be to file your return as soon as possible so that you will know if you owe more or (hopefully) you didn't owe at all.
To avoid this in the future you should make Estimated Tax Payments each quarter. Your tax professional can help you determine what this amount should be. But if you self-prepare you will want to take the amount you owed this year and divide by 4. This is the simplest way to come up with your estimated tax payment amount but I highly recommend finding a tax professional to help you.
Estimated Tax Payments are due as follows:
Payment 1 - April 15
Payment 2 - June 15
Payment 3 - Sept 15
Payment 4 - Jan 15 (following year)
Remember, you CAN file an extension to file later but you CANNOT file an extension to pay any tax due.