Single USB port: Depending on your PC's capabilities, you will be able to power Sol with a single USB port at a good brightness. Simply plug in your master half to the PC, and the interconnect cable between the two halves.
Two USB power sources: Your Sol can be given extra power through the slave half's open PC port. Since the "master" switch is off, that half won't be able to communicate with the PC, and will only draw power. You can also use a phone charger/batter pack.
USB Fusion: In order to get max brightness with a single cable, USB Fusion may be used to power Sol. The USB-Fusion page has more details.
If you're using two USB power sources, keep mind that they will be in parallel with each other. While this approach has been done many times (see any USB DVD drive with 2 usb plugs), it's still not "kosher". For the most part, you shouldn't have any problems. I've been using two for a few weeks now with no issues.
Sol has 88 WS2812B LEDs. According to their spec sheet, they can pull up to 60mA when all 3 R,G,B LEDs are on. This will be referred to as "full bright white", and can theoretically reach 5.3A for just the LEDs. If you keep saturation at 255 (100%), the LEDs will only use one LED (or a combination of two or three) at full power, so the current will be closer to 20mA. In order to reach full bright white, you must reduce saturation to 0, and increase brightness to 255.
In practice, I haven't seen my Sol pull more than ~1.6A at max brightness with rainbow animations. Assuming 100mA for the controllers, this results in ~17mA per LED. When decreasing saturation, the current will go up, past 3A. This is very bright, and almost unusable in a moderately lit room. I'm sure that most of you will find yourself turning the LEDs down to 50-60% brightness, depending on your keycaps.
Finally, not all USB ports are created equal. Officially, Sol is USB 2.0, and no port should give it more than 510mA. In practice, I've found that most type A ports will give me up to 600mA. The dedicated 3A charging port on my motherboard can deliver up to ~2.6A, on both type A and C. The front panel ports can do up to 1.1A. Depending on how bright you want your Sol to be, you'll want to check around your PC to see which ports will drop the voltage too low and fail the controller on Sol. It's a pain to test this without a USB multimeter, but you can count the steps for brightness (there are 10) to keep track.
In summary, everyone will have a different experience with max brightness for Sol. Your limitation will be dependent on your port's ability to deliver high current without dropping below 4.3V, where the controller will stop working.
If your controller fails from bright LEDs, have no fear! Unplug Sol and your slave half, then plug in just the master half and reduce brightness. If that still doesn't work, unscrew the LED plate from the bottom to manually remove the current draw.