To learn how to calculate mean squared error in a spreadsheet, see the file on my web site, "ForecastErrorAnalysis.doc".
Given that you have calculated mean squared error in a second order exponential smoothing spreadsheet, you can then adjust the values of your two smoothing constants to see what values minimize mean squared error.
You can use Excel's Solver to minimize mean squared error. Set the solver to minimize the MSE cell, by changing the alpha and beta cells, subject to alpha and beta between 0 and 1.
Excel's Data/Table command can also be useful to see how different input values affect the MSE. What this command allows you to do is to try inputing different values into a cell (a one-variable data table) or into two cells (a two-variable data table) and then to create a table that shows a calculated result for every set of input values.
To see how this works for a one-variable data table, open the practice file on my web site, "DataTableExample1.xls".
To see how this works for a two-variable data table, open the practice file on my web site, "DataTableExample2.xls".
For analyzing forecast error in second-order exponential smoothing, you could use a two-variable data table to see how different combinations of alpha and beta affect MSE.