You don't need to do anything until you file your 2016 tax return in early 2017. Yes, you just pay capital gains tax. But, capital gains tax is part of your income tax. Long term capital gains are just taxed at a lower rate than "ordinary income". For many people that rate is 0% (people who didn't owe any taxes probably qualify for 0%)
That said, not owing any taxes last year doesn't exempt you from advance payments. But having a zero tax liability (line 56 of form 1040 or line 39 of form 1040A) in 2015 does.
