Hello @Mike Kiser and thank you for your question.
You can use pipeline expressions in the body of your web activity. Suppose the date you want to use is the day the activity is run:
@concat('{"lastRunDate":"',formatDateTime(utcnow(),'yyyy-MM-dd'),'"}')
or you want to put a parameter as the body
@string(pipeline().parameters.preparedBody)
You can open the expression editor by clicking in the body textbox, then mousing below. (see picture)
To change an expression, once you have entered one, just click the body textbox again.