At the table, make the field type Date/Time, then look below for the properties of the field, and change the Format property to Short Date. In fact, the Date field could be defaulted to Date() rather than Now.
Now, as for the code, you want the code in the OnLoad event of the Switchboard. What it sounds like is your module is defaulted to Full Module view. I don't like view for most everyday programming because it gets to be a lot of chaos. It can also cause problems like what you ran into. You pasted the code at the bottom of the rest of the code that you saw, meaning that you did not put it in a procedure at all.
If you want to turn off the Full Module View (believe me, the layout will make more sense to you), click on Tools>Options, and find the checkbox marked "Default to Full Module View." Uncheck it. Now you will show one procedure at a time.
Now go back to Access, back to the properties of your switchboard, and find the OnLoad event. You should already have the words "Event Procedure" there, because the first time you tried to paste the code, it created the procedure, even though you didn't paste your code there. Click on the build button to the right of the field, and then paste your code between the Private Sub declaration and the End Sub line.
(Also, delete the code from where you originally pasted it).
You can move about in the modules in your project by double clicking on the module and then choosing the object and procedure. I had you go back to the Switchboard properties to make sure that "Event Procedure" was listed there. You can navigate to the event procedure for the form in the VBE window and put all the code there you want, but it won't run until you tell the object that in that Event property, it should run the Event Procedure.
HTH