Excellent question!
You have now entered the realm of Estimated Taxes. As you know, federal income taxes (plus state and local where applicable) are automatically withheld from your paycheck. Taxes on investments, at least by default, are not withheld from interest, dividends and capital gains from investments. The government requires you to handle those yourself.
There are two ways to handle this:
1) Use a W-4 with payroll to increase the amount of income tax withheld from your pay. This can be in the form of reducing your exemptions (which would increase the amount of federal income tax withheld by about $3000 by the end of this year) or asking that an additional fixed dollar amount be withheld from each paycheck. Then, come tax time next year, you would file your taxes and that extra tax withheld would be applied against all the other previously untaxed income. So long as at least one of (a) your April 2017 tax due payment (if any required) being less than $1000, (b) at least 90% of the total tax calculated on the 2016 tax return due April 2017 has been covered by your withholding, or (c) an amount equal to or greater than 100% of the total tax calculated for the return you are filing this April is collected through withholding in 2016. (That 100% may be 110% if you are sufficiently wealthy.) These criteria are documented in the instructions for Form 1040-ES (https://www.irs.gov/pub/irs-pdf/f1040es.pdf). A similar set of criteria apply to state income tax, though the percentages may differ, e.g. Colorado only wants to see 70% instead of 90%.
2) Alternatively, you can file estimated tax payments separately from your paycheck and work. This is done on a quarterly basis. (So typical --- to the government a quarter isn't 3 months. The "quarters" are Jan-Mar, Apr-May, Jun-Aug, and Sep-Dec. This is a bit of financial chicanery so that they maximize the amount of tax money that comes in before the yearly budget cycle closes at the end of June and make it appear that the budget is more balanced than it actually is.) The 1040-ES link above has the instructions, worksheets and forms you can use to calculate how much you need to pay in order to avoid underpayment penalties. You can use TurboTax to do these calculations, too. Search for "estimated tax" in the product. You might also peruse IRS publication 505 (https://www.irs.gov/pub/irs-pdf/p505.pdf) if you want to learn more.
You can ballpark the tax due on dividends and long term capital gains by multiplying the gain by 15%. (It can go as low as 0% for folks in the lowest income bracket.) Interest and short term capital gains are taxed as ordinary income --- you can use 25% to ballpark that. If the total investment tax falls well short of the $1000 threshold, you most probably won't need to send in any extra payments before next April, but you might want to go ahead and send in estimated tax payments or increase the amount withheld from your paycheck so that the 2017 April bill doesn't grow larger than you would be comfortable with paying all at once.
