You can calculate the different species if you know one or the total of the species and at least the pH. The more info about the water you have, the more accurate are the values. You can use a geochemical modeling program such as PhreeqC (http://wwwbrr.cr.usgs.gov/projects/GWC_coupled/phreeqc/) for it.
You can also use the pKAs listed for it and calculate the concentrations as a function of the pH, but the modeling will be more accurate as it also takes temperature and salinity into account.
The basic equations for the calculations based on pKA are
K*1= [H2CO3]/pCO2
K*2= [HCO3-][10^-pH]/[H2CO3]
K*3= [CO3 2-][10^-pH]/[HCO3-]
With K*1, K*2, and K*3 being the 3 dissociaion constants
As Niko Finke said, you need to know two of the following parameters to completely describe the inorganic C system: alkalinity, total DIC, partial pressure of CO2, and/or pH. Once you have those measurements, you can use a variety of computing platforms to make all the calculations:
• as an application on your computer (http://pubs.usgs.gov/of/2010/1280/), or
• as an iPhone app (http://itunes.apple.com/app/co2calc/id407782321?mt=8).
On the other hand, if your question is about how to measure (in the field or lab) the concentrations of the various species in the carbonate system, I suggest consulting the "Guide to best practices for ocean CO2 measurements" (http://cdiac.ornl.gov/oceans/Handbook_2007.html).
You can employ a CO2Calc -a Seawater-Carbon Calculator for Windows, Mac OS X, and iOS (iPhone) - provided you have at least two physical (Salinity and Temperature) and two carbonate (TA and pH) parameters.