I'm a United States citizen, however I will be living outside US for the next few years. I still have a US brokerage account. Will I still be charged capital gains tax for trading US stocks with my US brokerage account while I'm living outside US? If so how much?
What ChrisinEdmonton told you is perfectly correct: you have to file US income tax returns on which you declare (and are taxed on) your worldwide income regardless of whether you reside in the US or elsewhere. That is, your income in your country of residence must also be declared on your US tax return and you are obligated to pay US income tax on it even though that income might have been taxed by that country. There are, however, a few reductions possible. You can deduct (some of) the foreign income taxes paid from your gross US income in arriving at your taxable income (which will reduce the tax due) or you can get a tax credit against your US income tax for taxes paid to foreign governments. There is also a limited exclusion for income earned abroad on your US tax return. See, for example, Taxpayers living abroad or Publication 54: Tax Guide for US Citizens and Resident Aliens Abroad. Note in particular that there ares no special consideration for capital gains.
The US has tax treaties with many countries (and Double Taxation Avoidance Agreements (DTAA) with others, usually in cases where the US Senate refused to ratify a treaty) that specify that income generated in each country will not be taxed by the other. There also are various categories of income (pensions, social security payments etc) whose tax treatment is spelled out in these treaties. Begin with Publication 901 to find out more details about tax treaties. Note however that Publication 901 says
Tax treaties reduce the U.S. taxes of residents of foreign countries. With certain exceptions, they do not reduce the U.S. taxes of U.S. citizens or residents. U.S. citizens and residents are subject to U.S. income tax on their world-wide income.
while Publication 54 says
Treaty benefits generally are available to residents of the United States. They generally are not available to U.S. citizens who do not reside in the United States.
Note also that you will likely have bank accounts, brokerage accounts, etc in the country of residence, and so you need to declare the existence of these to the IRS as well as the Treasury Department. If the total value of these assets is less than $10,000 during the entire year, then no reporting is necessary. Search for FATCA, FBAR and FinCen to find out more about this. You might find it useful to read the sister site expatriates.SE.