How to connect IR Transmitter and Receiver Module?
The device in the question is commonly sold on aliexpress.com and the likes of ebay.com.  As you might guess there is little in the way of documentation.  Without documentation we can only speculate.  As such, I expect that the module handles all the modulation and demodulation.  It is likely all you need to do is use the Arduino serial library and connect the TX and RX to the Arduino's RX and TX pins.  However, if you would like to preserve the function of these pins for use with the Arduino Uno's USB port, you can use the Arduino software serial library which will "emulate" a serial port an an unused (alternate) set of pins.

(This is an example of a similar well documented device with access to the schematic and source code.  Armed with this type of knowledge you can turn this device into what ever you want.  In other words, you probably don't even need an Arduino.  You can just program this device and be done with your project.)