I'm a U.S. citizen, unmarried, and living in a small Asian country. I am trying to figure out whether I earn enough to need to file a U.S. income tax return this coming April 15. My income isn't very high. I work part-time, which is actually enough to support me here. And the currency here is valued fairly low against the U.S. dollar. So, am I supposed to calculate the exchange into U.S. dollars when figuring out my tax obligation? How? And as of what date – the date I earned it, or the date I'm figuring out my taxes?
First off, congratulations on being one of the rare U.S. citizens living overseas who understands that the U.S. government continues to demand tax reporting and, in some cases, payment from you. (For a more detailed explanation of these obligations, see Overseas American Citizens' Obligation to Pay U.S. Taxes.)
It sounds like you are hoping to make use of the general rule that U.S. citizens (whether living in the U.S. or another country) need not submit a tax return if their income is below a certain threshold—$101,300 for tax year 2016.
For U.S. tax-reporting purposes, you must convert any foreign currency you earn into U.S. dollar equivalents. Most people use the yearly average exchange rate between the U.S. dollar and the foreign currency they receive to calculate this. The IRS lists a few yearly exchange rates on the Yearly Average Currency Exchange Rates Translating Foreign Currency into U.S. Dollars page of its website.
Note that there is no "official" exchange rate you are obliged to use for this calculation. Any posted, "consistently used" exchange rate—like those utilized by major banks—is acceptable.
There are situations in which it is appropriate to use an exchange rate other than the yearly average rate. For example, if you had income that was the result of a one-time event, like the sale of your house, you can use the actual exchange rate for that exact day in calculating that particular portion of your total income. Detailed historical exchange rate information is available on the Treasury Reporting Rates of Exchange page of the Treasury Department's website.
You need to use the exchange rate in effect for the tax year in question, not the rate at the time you're actually filing your tax return (most people file their return before April 15 of the calendar year following the tax year for which they are figuring their taxes).