To run Conqu on Linux, you need Adobe AIR. If you already have it, then you simply double click on Conqu's downloaded file. Otherwise, install AIR first:

1. Download http://airdownload.adobe.com/air/lin/download/2.6/AdobeAIRInstaller.bin Move it to your Home folder
2. Open the terminal and type sudo ./AdobeAIRInstaller.bin
3. After the installer runs successfully, download and install Conqu from http://conqu.com/download/get/desktop/linux