You'll need to file your income tax in March/April next year, and you will get your notice of assessment probably within a month. You'll start paying tax then, either as a lump sum, or spread over 12 months via a GIRO deduction.
You need to ensure that your contributions to SRS are received by 31st December if you intend to use SRS to reduce tax. But you don't need to do so if you don't forsee that you will have a lot of tax to pay. Usually people would use SRS if they would fall into the 7% or 11.5% tax bracket after accounting for all relevant reliefs.
IRAS has an income tax calculator you can use to estimate your payable income. Play with the figures to see if SRS works for you, and if so, how much.
The link should give you a better idea.
Your income for this year will be assessed next year and income tax payable next year.
If you intend to use SRS to deduct from your taxable income, you have to open an SRS account and contribute before 31 Dec this year.
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