Hi Mark,
 
Yes, a hydrometer is by far the quickest and simplest way to measure
salinity.  It's a very simple device, essentially a glass tube, wider
at one end, sealed at both ends, and with a weight permanently secured
inside the wide end.  When you place it in water, it floats
vertically, with the weighted end down.  Enclosed inside the narrow
end is a numbered scale.  The more dense the water (that is, the
higher the salinity), the higher in the water the hydrometer floats.
The salinity can be read directly from the numbered scale, at the
air-water interface.  Scientific supply houses carry them, usually
about $15.00 to $20.00.  Make sure you get a SALINITY hydrometer
though (also called a salinimeter).  Hydrometers are also made for
many other purposes such as measuring sugar, acid, or alcohol
concentrations, oil densities, etc.  They all work the same way, but
are calibrated for the specific purpose for which they were made.
It is rather difficult to get a measurement by immersing the
hydrometer directly in the ocean and trying to read it.  You would
want to have a glass container in which you could take a sample of
the water, then float the hydrometer in the container.  A glass
laboratory graduated cylinder works very well.  It can be a bit
cumbersome carrying this glass apparatus in the field, and
hydrometers are fairly fragile, but it will do the job if you want to
carry it with you.
 
Paul M.