How does one go about exporting games from the English tygem client to one's computer?

I play out the games on an sgf editor.

Due to the time settings I like to play at and the fact that I would prefer to concentrate on only the game, this option is not feasible for me.

During or at the end of a game you can click menu->save game. It is on the bottom right, book-like icon.

Alternatively if you open your user info, you can see a list of all your games. Double click one, and it opens in a small window, with a save button. However this button does nothing for me. Let me know it is functioning for you.

It is in gib format. You may use gib2sgf at (open/save with text editor) http://sowhat.ifdef.jp/SGF/
Or there might be other converters you can find.

So far as I know that bottom also does nothing when I click on it. I will, however, start trying to save my games when I play them as you previously mentioned. Thanks for the advice. If anyone else has any other solutions, please feel free to post them.

The client just needs an upgrade. It seems outdated, e.g. the latest news are from 2012. If Tygem continues to show disrespect to the western client then people outside Korea will move on.