To add a stamp to a PDF document in Adobe, select Tools in the upper left corner of the window, then select Stamp.
Select the Stamp drop-down from the top of the window and select the type of stamp you want.
In the below example, I'm using a Received stamp. Adobe automatically fills in the date and time for you.
Adobe will ask you for the information you want to include in the stamp. You can check Don't show again and Adobe will know to use the same information for future stamps.
Place your stamp, save the document, and you're done!