When you record your spectrum, the first thing to do is make a table of the positions of the laser and iodine fluorescence peak positions. The identity of each of the peaks may be labeled by the vibrational quantum number of the final state of the transition, v". I make a data table with the first column the quantity v"+1/2 (since this is what we wish to plot) and the second column the wavelength of the transition starting with the lase line. I recorded 36 transitions; How many did you get?
The wavelengths of the transitions are now placed in column two but it is the photon
frequency (which is proportional to energy through Energy = Planck's Constant * Frequency).
Convert all the wavelengths from 
to frequency in wavenumbers (cm-1).
Because the index of refraction of air is not exactly unity, the conversion between wavelength and
wavenumber is not simply an inversion, but requires precise tabulation of n for the conditions of
our laboratory. We are going to ignore this correction in this lab because the effect is almost
within the expected error of the measurement. So I have made a third colum which is the
wavenumber of the transition calculated as 108 / (wavelength in )
So now our data table needs the vibrational energy differences in the fourth column. subtract the adjacent transition frequencies from the third column and place them in the fourth column. Your top portion of your data table should look something like this:
What remains is simply to plot the data as pairs of points with column one providing the horizontal coordinate and column four providing the vertical. A spreadsheet program like Quattro or Excel is ideal for such a task. Typing the numbers you get from your spectrum into such a program will give you a plot that looks like this:
Whether you graph by hand or with the computer, you need to perform an analysis of the data as a fit to a straight line. The slope and intercept of the best fit line as determined by my spreadsheet program looks like this
Having the equation for the best fit line to the data, we can extrapolate to the highest vibrational level in the potential. At the top of the well, the vibrational first difference will go to zero. The value of the largest v" below the x intercept of the Birge-Sponer line is the quantum number of the last bound vibrational level in the ground electroniuc state. This is what the Birge-Sponer line derived from my data looks like:
The area under the Birge-Sponer line is equal to the dissociation energy of the molecule, D0 as referenced to the zero-point vibrational energy level. You should prove this in your report(it is proved in Atkins). The area, and thus the dissociation energy, may be calculated from the x and y intercepts of the Birge-Sponer line.
The spectroscopic constants such as the vibrational frequency 
e
and the first order anharmonicity constant, exe may
be determined directly from the fit to the Birge-Sponer line.
The anharmonicity, exe, is equal to the
negative one half of the slope.
The vibrational frequency, e, is the y intercept
plus the anharmonicity constant exe