A good starting place is to join the Singapore Screenwriters' Association...www.screenwriters.org.sg
They often run pitching sessions with local producers and various workshops and feedback groups. If you make yourself useful to them by helping organise things you will be first in line if opportunities present themselves.
Also check out the www.substation.org They stage a lot of creative events from Short film showings to workshops and so on.
And at the moment there's www.screensingapore.com.sg This happens every year and you can submit proposals to them and if you are chosen they will let you pitch to various producers they bring in from around the world. And in December there's www.asiatvforum.com And they run a similar scheme.
It's worth getting tickets to these forums as you get to go to lots of parties and meet various people in the industry. And they run various seminars discussing media issues and where the market is going at the moment.
By the time you've done all this you will have plenty of connections in the industry and then it is all a matter of coming up with the timely project! And that's the toughest part of it.
It is easy to schmooze and talk the talk, but far harder to actually deliver the goods. And breaking into an industry always requires that first of all you demonstrate you can do the job. But a lot of the job of this industry come in the form of producing material that can be made rather than producing material that should be made. Which is why you need to be talking with people who are at the cutting edge of the market place and trying to understand their needs and how you might shape your ideas to fit theirs, without destroying your creative integrity.