OK, here's a quick introduction....
1. If you haven't reviewed it already, start with
IRS Publication 54. It's a fairly comprehensive and detailed summary, straight from the IRS. Publication 54 is a bit dense, though, so if you have follow-up questions, feel free to ask.
In tax year 2015, assuming your filing status is Single, in most cases you were not required to file a U.S. tax return unless your total, worldwide, gross income was greater than US$10,300. (In tax year 2016 that filing threshold will be slightly higher, adjusted for inflation.) If you had income from self-employment the limit may be lower. Note that even if you are not required to file a tax return, there are a couple occasions when it still makes sense to do so.
If you were required to file but haven't, don't panic. The IRS offers a "Streamlined Program" to get caught up. At least for now, if you qualify and if you follow their instructions, the IRS waives penalties. A very low rate of interest (3%/year) is still charged if you're late paying any tax that you owe.
Even if you are required to file,
generally speaking a full-time overseas resident will not owe any U.S. tax (and of course no interest either) unless:
(a) Your gross income from work exceeds about US$110,000, or
(b) Your total gross, worldwide, non-work income exceeds about US$10,000, or
(c) You have non-trivial self-employment income, and you have not contributed to the social insurance program of a country that has a social security treaty with the United States. (Singapore does not have such a treaty, unfortunately.)
Also, for conditions (a) and (b), your non-U.S. income tax rate must be lower than your calculated U.S. tax rate. If your non-U.S. income tax rate is equal or higher, you will not owe U.S. tax. Income tax rates in Singapore are generally lower than U.S. rates, so you can ignore this caveat in Singapore.
I do not recommend trying to file your taxes manually, using the IRS's forms directly. Interview-style tax preparation software is quite helpful, and there are even free options. (For tax year 2015, H&R Block has/had a free online edition suitable for the vast majority of U.S. citizens living overseas.)
2. If the total value (adding all together) of your non-U.S. financial accounts reached at least US$10,000 at any point in the year, you're required to file
FinCEN Form 114 for that year.
3. If you are a young adult male, be sure to register with
U.S. Selective Service.
4. There's a U.S. federal election in early November. Perhaps you've heard about it.

Visit
FVAP.gov now to find out how to register and vote, if you haven't done so already.
....And with those four items covered, you should be "caught up" as a U.S. citizen living overseas. Welcome back!
