How do I select an entire row in Excel?

The shortcut to select a complete row is ShiftSpace.

Similarly, the shortcut to select a complete column, press CtrlSpace.

You can also select the whole row by clicking on the row header, as shown in this gif. This works for column headers too.

Similarly, to select only the contiguous cells with data in them, i.e. not every cell on the current sheet...

CtrlShift+right arrow will select the row

and

CtrlShift+down arrow will select the column

Incidentally, choose up, down, left, or right depending on where you are on the sheet. The keyboard combinations above will select in the direction you hit from the selected cell as the starting point.