EMT low power unfortunately is not well documented but quite simple. How low of a power the device goes into depends on what interfaces are open and what device the Sketch runs on.
The quick reference:
If all Sketches are in delay() the idle loop is entered. The idle loop is a TI-RTOS task that consults the power manager and then determines what level of low power it can go to.
Make sure that all unused pins are in the appropriate state according to the datasheet. Usually this is output high.
Make sure that sensors that are connected are put into sleep mode if you intend to go to low power.
Make sure that you call the .end() function on peripherals. e.g. Wire.end(), SPI.end(), Serial.end(), etc. This releases the constraint that the peripherals .begin() functions sets in the power manager.
Use inter task communication interfaces to communicate to other tasks when low power should commence. Examples of the low power intertask communication can be found in the Energia examples under File->Examples->10.MultiTasking. Typically you would want to go for semaphore of Event.
Pending on a semaphore also acts as low power mechanism. If you pend, the task stops becoming runnable and wont execute again unless the semaphore is posted.
Hope this helps.
I do have low power example Sketches in the pipeline but I won't be able to get to the in the next month or so.