There are a number of approaches, going from expensive and easy, to cheap and more complicated.
First off, a 6N137 is an Optocoupler, and not a source of isolated power. Digital optocouplers are important for some of the designs that follow, but they don't supply power, which you can generate off of a USB bus with a DC/DC converter with isolation. The TI selection matrix for such devices is at http://www.ti.com/lsds/ti/power-management/isolated-dc-dc-converter-products.page
The easy way is to use a USB isolator, like the Adafruit implementation at
https://www.adafruit.com/products/2107. These are expensive. That device actually produces an Isolated power source that can provide 100mA of current (though I'm not sure that's enough for the Arduino -- you'd have to look it up)
The next way to go would be to leave your arduino under USB power, provide an isolated power supply for your analog side, and use an ANALOG Isolator to bring the signal to the ADC on your arduino.
An inexpensive analog isolater is the HCNR201 -- http://www.avagotech.com/products/optocouplers/industrial-plastic/specific-function/high-linearity-analog/hcnr201. Such things can be tricky to use, and will require op amps on both sides of your isolation.
You can also use ISOLATION AMPLIFIERS (http://www.analog.com/en/products/amplifiers/isolation-amplifiers.html) to the same effect, and they're likely easier to use. There may even be some that provide the isolated power.
The easiest way to do it, short of a USB isolator, is to power the arduino off-chip, put an external ADC in your system, and use digital isolators, like your 6N137. Or, you can use a serial bus isolator, like the ADUM1250 I2C isolator to bring the data to your arduino using digital means, which has the advantage of being useful on a bidirectional bus like I2C, if your ADC is of that ilk. Digital isolation is cheaper and easier than analog.
Each method will have advantages and disadvantages. My pref, though, would be to keep the arduino on the computer side, then you won't need to worry about clock noise spreading across your nice clean isolated ground. With the problems associated with analog isolators, this would push me toward using an external ADC and serial bus isolators.