The small/male/micro-B end of the cable goes in your phone, and whatever you're trying to connect goes in the big/female/USB-A end of the cable.
Connect your Mod to its USB cable, plug that into the OTG cable
Plug the small/micro-B end of OTG cable in to your phone
Turn the Mod on, and connect to it in the Serial Monitor app.
We have to force Arduino not to include any HID features. The way you do this is to edit the USBDesc.h file included with Arduino. On a Mac, this is found inside of the Arduino.app itself. From the Finder, right click on the Arduino application, and choose "Show Package Contents". From there, go through Contents > Resources > Java > hardware > arduino > cores > arduino and you'll find USBDesc.h (in the 1.5.x Arduino development environment, this file is found in Contents > Java > hardware > arduino > avr > cores > arduino).
Open USBDesc.h and edit it:
#define CDC_ENABLED #define HID_ENABLED
#define CDC_ENABLED /* #define HID_ENABLED */
You have commented out the line defining the HID_ENABLED variable.
You may have to quit and reload the Arduino app and then recompile your sketch for it to take effect.