The thing you need is a so called shunt resistor. A resistor can be thought of as a device, which turns voltage into current and vice versa. So if a certain amount of current (I) flows through the resistor, a proportional voltage (U) occurs across the resistor. An oscilloscope only measures voltage so in order to measure current we need the resistor to turn it into a voltage. The value of the resistor should be quite small in order to not impact the measurement too much. Usually 0.1Ω or smaller is used. The accuracy of the resistor directly affects the accuracy of the measurement so get a decent one.
Why measure current?
Power (P), what you want to measure, is calculated as voltage times current. Since oscilloscopes can't measure it directly we need to calculate it. The complete formula is in the bottom of the picture.
What is the second probe for?
USB is usually 5V which we could simply plug into the formula and call it a day. But since you want to use a computer as the power supply, which output voltage can vary quite a lot, it is best to measure it as well.
What do the colors of the wires mean?
A USB cable generally has four wires. The green and the white wire are data wires, which you should simply leave connected. The back wire is the ground or negative wire and the red is the positive wire.
Is there anything else to keep in mind?
In general there is not so much you can do wrong here but when you are using a mains powered oscilloscope the probe ground is tied to the mains ground. This can cause a ground loop when the laptop is also plugged into the mains, which you generally want to avoid. So just leave you laptop on battery during the measurement and everything should be fine.
