I think this book by Nolan&Wallach, "Representations and Invariants for Classical Groups", google preview [here][1] is very good. Only a few chapters in this book are 100% relevant to the topic, but if you focus on them you should get a good basic picture. 

Else if you are interested in invariant theory for unipotent groups (often if you try computing invariant theory for direct sums of representations of reductive groups, you will end up with something involving unipotent groups as well, for instance), there is a good paper [here][2] , it is somewhat algorithmic though. 

I do not know how to get the links right, please correct the awkward linking if possible.


  [1]: http://books.google.com.au/books?id=KBFoV2jpnPUC&dq=Nolan+Wallach+Invariant+Theory+classical+groups&printsec=frontcover&source=bl&ots=YyE9WR620i&sig=t9Sx3f3wi-vk7C-i0D_HCVbZUFk&hl=en&ei=RsctS9DpI4yOkQXTs9DXCg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CA0Q6AEwAA#v=onepage&q=&f=false
  [2]: :%20http://journals.cambridge.org/action/displayAbstract;jsessionid=2AF426FA9416AD7290897BBDE9CB1F10.tomcat1?fromPage=online&aid=57495