Select the date column or the entire data range
Go to the Data tab
Click Sort A to Z for oldest to newest
Click Sort Z to A for newest to oldest
If prompted, choose Expand the selection
In the Sort dialog, select the column with dates
Choose Sort On as Cell Values
Choose Order as Oldest to Newest or Newest to Oldest
Click OK
Format the cells as Date if the sort does not work correctly
Remove any blank cells or mixed text values in the date column before sorting