I have played some games of TwixT, but I have not managed to win a single game. I know something about Hex, and my approach to TwixT has been that it is a game similar to Hex, but this approach has not been fruitful. So are there any strategy guides in the net that I could read? Or can someone give some other pointers to strategy? I really would like to learn TwixT.

There is some info in the Twixt wiki

TwixT is more tactical than Hex, which is a little more strategical especially on large boards.

There are some basic patterns that you need to learn, you should try to watch and analyze some games of strong players to see how they manage to build their games.

Puzzles in interactive format

Hub link on BGG. Check out the forums, the files, the images, and the web links.

Download a computer opponent written in Java. You could take a handicap if it is stronger, or give one if it is weaker.

Every completed game has an analysis link where you can post questions.

Please ask me if you have any specific question or problem with regard to any of this.