A batch of compost is finished and decomposed when:
The raw materials are no longer recognizable as the raw materials you put in: grasses, twigs, coffee grounds, banana peels, weeds, and such. Although, some small pieces may still be recognizable.
It looks similar to peat moss, or potting soil.
The material is rich and crumbly.
The compost is no longer warm to the touch. It is no more than 10 degrees F warmer than the outdoor temperature.
Where did it go? Finished compost shrinks to about 1/3 of the original volume. It is denser, more compact, and has less moisture content than the original materials.
Note: It is okay to use compost a little before it is completely finished, as long as it is no longer hot.