What we have here is a pair of nRF24L01+ 2.4GHz Wireless Communications Modules which you can drive from an Arduino.
Short version, wire these up to your Arduino, and using one of the libraries available (Mirf or RF24) you can communicate wirelessly.
These devices require 3.3v power, but signalling is 5v tolerant. Please note you need a good strong stable power supply - even a slightly weak power supply can make for no communication and much head scratching, the modules draw a reasonable current when actively transmitting, and not much when not. A couple hundred pF cap across the VCC and GND inputs to the module are a good idea.
Google for nRF24L01+ for more information, these modules are quite common.
The Arduino library under most development is I believe the RF24 library, which is available in the Arduino LIbrary Manager ( Sketch > Include Library > Manage Libraries and then filter for RF24) which you can read about here
Once again, the most common form of problem people have using the NRF24 modules is power related, you need a strong stable 3.3v power supply feeding them.
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