Hi paul_kiss,
To take a screenshot, as Caius has said, you can press the "Print Screen" key on your keyboard. The shot will be saved into either "C:\Program Files\The Creative Assembly\Rome - Total War\tgas" should you have Gold edition or "C:\Program Files\Activision\Rome - Total War\tgas" should you have a standard version of R:TW, not Gold. Unfortunately, they are stored as a .tga file which is un-openable in standard windows programs and, sadly, also cannot be published on most image hosts. To open them and publish them they need converting. One of the most popular of these programs is Infranview, yet there are many others out there which can be easily located through a quick Google Search for "tga converter".

Unfortunately, should your tree be large, you will have to take multiple screenshots of the family tree scroll for it to work. Also, again problematic, will be that, if you want to show generals stats and traits, you will again have to take multiple screenshot. I do wish that R:TW did include a similar function, but, most unfortunately, this is the best alternative that we have.

If you require any more information then do not hesitate to ask. Hope this helps, sorry for bearing bad news, cheers!