To compare input and output data in ROOT programming, users can overlay two histograms in the same diagram. While it is possible to use the ROOT browser, it is often easier to use the command prompt or write a script for execution. ROOT is built on C++ libraries, so understanding basic C++ commands is essential. Users can utilize commands like "Draw('SAME')" for histograms, and additional examples can be provided for clarity. For beginners, detailed explanations of these commands and plotting techniques are crucial for effective data visualization.