First, ensure your script begins with the correct hash-bang, 
e.g. #!/bin/bash

Then make sure the .sh file is executable -
    Open a terminal using Ctrl+Alt+T or from the applications menu
    Navigate to the location of the .sh file. e.g. 
    cd ~/location/to/my/file
    Run  
    chmod u+x .sh
    , or if permission is an issue, 
    sudo chmod u+x .sh 
    and enter your password to confirm
    Alternatively, you can right-click the .sh file from the file 
    browser and update permissions via the Properties option