One way to do this is to archive the NSAttributedString value. Outline sample code typed directly into answer:
NSTextView *myTextView;
NSString *myFilename;
...
[NSKeyedarchiver archiveRootObject:myTextStorage.textStorage
toFile:myFilename];
To read it back:
myTextView.textStorage.attributedString = [NSKeyedUnarchiver unarchiveObjectWithFile:myFilename];
That's all that is needed to create and read back a file. There are matching methods which create an NSData rather than a file, and you can convert an NSData into an NSString or just insert one into an NSDictionary and serialise that as a plist (XML), etc.