This is something I should have probably done before as I left Singapore to go back to France about 2 months ago.
It definitely was a great experience and for the record just go see by yourself: it is the best thing you can do :)

Regarding all the questions I had about getting a job/internship in Singapore here are some precisions:

-First if you're French (but non-French people can find an equivalent website) the French Chamber of Commerce in Singapore is a must-visit website where you'll be able to find informations, direct contact number, emails addresses of any french company currently in Singapore. A research by field of activity can also be done..

-Second. If not already done, go register on Linkedin. It is a networking website, to make it simple: a facebook-like for professionnals. You create a profile - pretty much an online resume - and you can look for people working in the fields you're interested in, in the companies that attract your interest, or for anybody working in Singapore.. This is a really powerful tool: the more people you know, the more people you get access to... And it's all free (you can purchase some options to be able to contact more easily but it is far from being required for a normal usage). One interesting features of linkedin in that you search a company, get a short description of it, and see all the people currently working for it..

-Last thing to talk about: visa requirements. There is tons of foreigners working in Singapore (if I'm not wrong about a 1/4th of the overall population) so I bet it's not that difficult to get a working pass there (without comparison to getting one in the US). It took me a month and a half to get mine: all I had to do is apply for the Singapore Work Holiday Programme on the Ministry of Manpower's website. You can also have a look to the WHP dedicated webpage.

This is it. Hope this can help. Enjoy your time in Singapore if you ever get the chance to work/study/live there.