how do you determine the ending balance of a capital account?

Four things affect capital: Revenues (+), Expenses (-), Investments (+), and Withdrawals (-). You will need to know those four things.

Therefore,
Beginning Balance
+Investments
+Revenues
-Expenses
-Drawings
=Ending Balance

Remember that Revenues less Expenses = Net Income. So you may need to add Net Income (or subtract Net Loss) rather than doing those separately, depending on the information you're given.