This app was mentioned in 2 comments, with an average of 2.00 upvotes
If using Android: https://play.google.com/store/apps/details?id=sk.i2m.mylog
I just use the above app to tally up the miles driven while working, multiply by the IRS milage deduction ($0.575, I believe), subtract that number from the take-home pay I made during each quarter.
Most of the time, the amount is pretty miniscule but, I'll pay 25% of that amount on the IRS website. Here's an example:
Jan-March '16:
Total miles driven while working (via Mylog app): 1,964
IRS deduction: $0.575 X 1,964 mi = $1,129.30 in deductions
Total take-home from Uber = $1,322.44
$1,322.44 - $1,129.30 = $193.14
25% X $193.14 = $48.29 to pay the IRS before April 15 (day quarterly estimated taxes for Q1 are due)
Your 1st year doing this, the IRS doesn't impose penalties for waiting to pay estimated taxes until the end of year. After year 1 of your business, they will impose penalties if you don't pay the quarterly estimated taxes.
Hope this helps
Or you can just use this for free