The best way I've found is a free bit of software called CopyText - you can find it here. The site and the software looks safe; I haven't had any issues.
The program is simple to use but you MUST read the Readme.txt for details on setting up the hotkey to capture the text.
Basically ...
1 - Put mouse cursor over the combat info box
2 - Press CopyText hotkey and the program window opens ...

3 - Press 'Copy all'
4 - Paste into document of choice - text, Word, Excel etc
There's some other options within the software but I haven't played too much with them.
Cheers