What is the long thin hand on most chronographs?

The long thin hand on most chronographs is often part of the stopwatch function.

Where is the true second hand on most chronographs?

The second hand on the watch below is the small subdial on the left portion of the watch face. On your watch the second hand may be one of the other complications on the watch face.

How to use a chronograph's stopwatch function? 

Pushing the top pusher starts the stopwatch, and the 'second' hand will begin to sweep.
Pushing the top button stops the stopwatch, and the 'second' hand will stop sweeping.
Pushing the bottom button after the stopwatch is stopped will reset the 'second' hand to zero.
Doing otherwise will activate the ‘lap’ function, resulting in the hand jumping to its current position which will continue sweeping until the bottom pusher is pushed again. 

If the chronographs are not resetting back to zero, see "resetting chronographs to zero"