There are a number of settings that affect Word's table size and actions.
First try this:
Right-click on the cell in the table (or select the whole table and right-click).
Select 'Table Properties...'.
In the Table properties dialog box select the 'Cell' tab.
In the Cell tab click the 'Options...' button.
You can check either ''Wrap text' or 'Fit to text'.
You probably want to use 'Wrap text', as 'Fit to text' changes the font size - usefull if you have occasional cells with text that is just a shade too long to fit.
Click OK out of the dialog boxes.
Alternatively select the 'Table' tab in the Table properties dialog box and click the 'Options...' button.
Check the 'Automatically resize to fit contents' box.
You can also manually resize row heights - with the mouse over the lower border of a row, when the mouse changes to two parallel lines, click the left mouse button, hold it down and drag the row to the required height.