Seeking advice and help in looking for a job in Berlin

Look on the internet for major companies in berlin, and register for their graduate programmes.

Find out the potential employers in your field and try to contact key persons there (e.g. through Linkedin or Xing).
Also, unsolicited (i.e. not replying to an ad) applications are very common and often successful in Germany.
And don't discount other locations - business is clustered in Southern Germany, not Berlin.
Of course some German language skills will increase your chances tremendously. There is a Goethe institute in Singapore.
(My wife is Singaporean, too, and we live in Stuttgart. You're welcome to send me more questions!)

Thank you for all the useful advice! Really appreciate it! Yes, beppi, I do have some questions and i'll send you a private message separately.