What type of script is it?
To run a script once per day in the background, you can create a launch agent for your account or for the system that will run the script in the background. To do this, create a plain text file with the following contents, and save it with the file extension ".plist" in the LaunchAgents directory (for instance "dailytask.plist").
You can do this by holding the Option key and choosing Library from the Finder's Go menu, and then navigating to the LaunchAgents folder. Keep this folder open so it will be accessible.
Next, open TextEdit and create a new document, then press Shift-Command-T to make it a plain text document, and then copy the following contents to the document and save it to your desktop.
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
<key>Label</key>
<string>local.dailytask</string>
<key>ProgramArguments</key>
<array>
<string>/PATH/TO/SCRIPT/GOES/HERE</string>
</array>
<key>QueueDirectories</key>
<array/>
<key>StartCalendarInterval</key>
<dict>
<key>Hour</key>
<integer>12</integer>
<key>Minute</key>
<integer>30</integer>
</dict>
</dict>
</plist>
Now change the text that read "PATH/TO/SCRIPT/GOES/HERE" to be the full path to the location of your script, so for instance if your script is called "myscript.sh" and is in your Documents folder, then you would put the following (replacing "username" with the short name of your account--ie, your home folder name):
/Users/username/Documents/myscript.sh
Next locate where it says Hour and Minute, and change these to be the desired time you want the script to run (hours are in 24-hour format).
With these changes made, save the document and then rename it so instead of having ".txt" as the extension, make the extension be ".plist" (confirm the change when prompted). Then copy or move the file from your Desktop to the open "LaunchAgents" folder.
With this setup, now log out and log back into your account, and the system should run the designated script at the appropriate time.
Do keep in mind to use AppleScripts you will need to specify more details instead of just the path to script as I mentioned above, or optionally you can have the path here point to a small secondary shell script that itself will contain a command to run the desired AppleScript or other script.
Lastly, the use of the LaunchAgent folder in your home directory means this script will only load when you log in, and will run under the scope of your user account. If you want it to run for all users or even if the system is at the login window, then you will have to use the global LaunchAgents directory in the Macintosh HD > Library folder.
If you run into any hurdles with this approach, post back here and folks will be glad to help you set it up.