How do I use a USB OTG cable to read a USB thumbdrive on Arduino Uno?
Not without getting your hands dirty or buying a shield.

Arduinos are configured by default as slave usb devices. Slave devices cannot connect to other slave devices, so connecting a thumb drive via a USB OTG cable is meaningless.

If you don't want to get your hands dirty, there is the USB host shield as suggested by @Kevin which should work.

If you do want to get your hands dirty, you can try flashing new firmware on the 8u2/16u2 chip on the Uno. This chip is what gives the main ATmega328 the ability to load programs and send serial output via USB. It can be reprogrammed to be various things: a joystick, a mouse, a keyboard.

However, it is not limited to slave devices, one can also program it to be a host. With a Due, being a USB Host for a mouse or keyboard is quite easy, but for other Arduinos you need to program the 8u2/16u2 chip.

Note that programming an Arduino to understand a USB mass storage device has not been done yet. There will be a significant amount of mucking through code if you wish to do this.

Basically, you use the LUFA library, specifically the USB Mass Storage Host class. I can't find anything apart from that doc page and the source code of the class (which is extensive), so I can't write up the code myself. However, you may want to take a look at this tutorial on making an Arduino joystick via LUFA to get started.