Highlight the row(s) that contains the data.
On the Home tab, select "copy." Do NOT select "cut."
Select the paste area that you want to use - do not overlap any of the cells in the "copy" or "paste" areas. So, if you're data starts in cell A1, and the first open cell on the worksheet is A14, you will want to select A14 on the original worksheet, or change to another worksheet and select A1 on the new worksheet before pasting.
On the Home tab, select the little arrow below "Paste."
Your data should flow down from your selected input cell.