Download the latest version zip file.
Extract all the files from this zip archive on your computer.
Create a new MySQL database at your website for ShiftExec. If you already have a database, and you can't or don't want to create another one specifically for ShiftExec, ShiftExec can easily make use of this existing database. The names for database tables starts with ShiftExec's own prefix thus they do not interfere with other applications.
Rename the db.rename_it.php to db.php, then open this new db.php file in your text editor and enter your MySQL database login information. The file already contains some sample values so it will be easy.
Decide in which directory you will be installing ShiftExec on your website. You would probably want to create a new directory. Upload all the files keeping their directory structure there.
Point your browser to the web page where you have uploaded the files. You will be transferred to the setup screen. Please follow the instructions on the screen.