To read the operating system clipboard, call the getData() method of the Clipboard.generalClipbooard object, passing in the name of the format to read:

import flash.desktop.Clipboard;
import flash.desktop.ClipboardFormats;

if(Clipboard.generalClipboard.hasFormat(ClipboardFormats.TEXT_FORMAT)){
    var text:String = Clipboard.generalClipboard.getData(ClipboardFormats.TEXT_FORMAT);
}

To write to the clipboard, add the data to the Clipboard.generalClipboard object in one or more formats. Any existing data in the same format is overwritten automatically. However, it is a good practice to also clear the system clipboard before writing new data to it to make sure that unrelated data in any other formats is also deleted.

import flash.desktop.Clipboard;
import flash.desktop.ClipboardFormats;

var textToCopy:String = "Copy to clipboard.";
Clipboard.generalClipboard.clear();
Clipboard.generalClipboard.setData(ClipboardFormats.TEXT_FORMAT, textToCopy, false);