Hi SBC,
Welcome to the forum! It's great to have another S'porean here!
Unless your VFT is next to a window in your study room which receives lots of light, I'm afraid that your current set-up is unlikely to provide sufficient light for the VFT. You need to shift it to somewhere that receives lots of light for the VFT to grow well.
Then, u need to water the VFT using the "water-tray" method, which essentially involves placing the pot containing the VFT in a tray of water. An impt note about the water: it must not be tap water or mineral water . It can only be distilled, RO or rain-water. Boiled water doesn't work as well (though there have been users who get away with that, though it's generally not recommended).
Where did u get the VFT from? If u got it from Far east Flora, it should be potted in pure peat in a fairly small pot. That's fine -- but the recommendation is for VFTs to be potted in a mixture of 1:1 peat and sand, so as to provide for better drainage. As the plant grows bigger, u could consider repotting it in a bigger pot.
The main problem with the VFT (and other temperate CPs) is their requirement of a dormancy. I have zero experience with this, so I'll leave it to others who have to voice their views. But the general agreement is that VFTs need a dormancy to survive long-term, and the only way to do that here seems to be to put the plant in the fridge for a few mths at the appropriate time.
Any other concerns can be answered here:
http://www.petflytrap.com/care.html