Dumping the text is one of the first steps in translating a game.
Essentially, you seperate all the text in the game, from all the other stuff (Code, movies, images, etc), and "Dump" it all into file(s).
After that you check to make sure it's all there, and that you don't have anything you don't need, then work to actually translate it.
In order to patch the game with the new text, you would essentially replace all the old text with the new, much like overwriting a file.
The methods to do this would vary from game to game. Some games use one or more files to store all the text in, so it would be as easy as replacing that file with the new one. Other games would actually require you to "inject" the information into a file. This could be done manually, or the people that did the translation could make a utility to do it for you.
EG
