What is the best way to find out how much sodium you lose during an
event such as running or biking.  There is so much hype about
replacing electrolytes - how do I find the right balance.

hawaii04

I am assuming you are asking about how much sodium is lost due to
sweating. As you may know, sodium is also lost in the urine. If you
could just clarify that one detail for me, I would love to answer your
question.

smart5450 (Elis)

I take a product called Celtic Sea salt during my training.   I am
trying to find out how many grams of salt I should consume per hour? 
I believe I would figure this out by looking at my sweat, urine, etc.

The condition you are concerned with is called "Hyponatremia"
or "water intoxication".  This is where the body's mix
of eloctrolytes/salts get seriously out of balance.  

This is a bad thing, as in extreme cases it can cause death.  The
body starts scavenging salt from the internal organs, leading to
organ failure and then death.  Fortunately this is typically only
a problem for extreme endurance events.  As an example, the U.S. Army 
reported 57 cases of hyponatremia in the period of time between
January of 1997 and September of 1998.  For details on this, and
the new guidelines on fluid intake to prevent it, see the ever
entertaining:
 http://66.102.7.104/search?q=cache:ag4JeEci72sJ:amsa.army.mil/1MSMR/1999/v05_n02.pdf+hyponatremia+army+deaths&hl=en

(The third item returned by Google when searching on "hyponatremia army deaths")

However, as to your question:

From http://www.rice.edu/~jenky/sports/salt.html

--begin quote--
Sweat contains between 2.25 - 3.4 grams of salt per liter, and the
rate of perspiration in a long, hot race can easily average 1 liter
per hour. So, for a 12 hour race, one could lose approximately 27 to
41 grams of salt. If the athlete replaces only the lost water and has
minimal salt intake, hyponatremia can result.
--end quote--

The military suggestions are to limit water intake to 1 qt per hour.  This
is probably your best bet, and unless you're doing an Ironman, don't worry
about the salt.

Google search: hyponatremia   (knowing the medical term really helped :)

Other links of interest:

http://www.honoluluclub.com/pulse.php?ID=31
http://www.emedicine.com/EMERG/topic275.htm

And even my own humble input into hydration:

http://www.bofh.com/other/ultimate/other.html#hydration

There are profesional sports doctors that can measure your blood
levels in different areas. I suggest you use this method. It is the
most reliable. Any sports center can refer you.
Stay Healthy!
Spinnster