If your tax liability last year - which is line 63 on Form 1040 for most people - was really $0 and that tax return covered a full 12 month period, then I see no need to make any estimated tax payments at all. You simply won't be charged an underpayment penalty as long as you pay your 2016 income tax liability on time.
If by "owed no tax last year" you are really saying that you didn't have to send a check in with your income tax return, (maybe even received a refund), that's not the same as having a 2015 total tax of $0, so in that case you should, probably, make an estimated tax payment by the January 2016 deadline. That's not guaranteed to have you not face any underpayment penalties, since the penalty is calculated on a quarter-by-quarter basis, but it should server to minimize any penalty.
Tom Young
