Android does not provide enough power to usb otg devices.
If your android smartphone does not provide enough to power up USB-OTG,
you can get a OTG Y-cable from amazon for $7.
You may need to install custom rom if your stock android does not support USB-OTG
The power the USB port outputs depends on your hardware. If a standard USB OTG adapter does not provide power to the USB device, your phone or tablet may not support USB OTG.
It's possible to make your own USB OTG cable with an external power source. You would basically connect the power providing wires in the USB cable to a 5V power adapter, and keep the data wires connected to the micro USB port on your phone. If something goes wrong making the cable you might break your phones USB port though!
If your phone or tablet was not designed to provide USB OTG (which is very likely if it doesn't provide power), your Android ROM will likely miss external USB support as well. The lack of software support might be circumvented by installing a custom ROM if one is available.
Some newer devices with large batteries allow you to power other devices but it's dependent on the hardware and software. Some devices are physically able to but manufacturers(and carriers) don't have it enabled. If you have a specific device in mind that you're trying to enable it for that would be helpful in finding out if it's even possible to turn it on(which would most likely require rooting your device and possibly a custom rom).
Also, some devices that do allow for power through their usb port don't send that much power. Most manufacturers expect people to buy a power bank or another battery than buy another phone to power a device, so if they do allow for power through the usb, it may only be enough to power something like a mouse, keyboard or small midi device.