How can I create an empty file?

There are several ways to create an empty file using AppleScript. The quickest one is the following:

set newFilePath to "disk:folder:file.txt"
open for access file newFilePath
close access file newFilePath

The open for access command, from Standard Additions, will create a new file in the specified location if it doesn’t exist.

From a shell script, you can also try this one:

do shell script "touch /path/to/file.txt"

And, finally, you can simply use the Finder:

tell application "Finder" to make new file at desktop

If you create a file using the Finder, you can also define some additional parameters. Eg:

tell application "Finder" to make new file at desktop with properties {name:"pic.jpg", creator type:"8BIM", comment:"Hi!"}