You can insert today's date at the current entry point in your file by choosing "Date Stamp" or by typing Command-D.
If you want the date to be automatically inserted at the beginning of the Note field, go to the "Preferences" under the Edit menu and check "Date Stamp Note Field". Today's date will appear at the beginning of the Note field followed by a space, so that you can start typing.
For suggestions on how to use date stamping with the Note field, see "Note Field".