It really depends how monkey proof your application need to be.
Is it enough to just return "Wrong date input"
or do you want to give more information to the user like "Invalid month value"
DateTime.Parse can be enough also be aware of DateTime.TryParse
I think you should print the expected datetimeformat like "yyyy-mm-dd" so the user does not have to guess.
Or you can ask 3 questions
This can be helpfull or really boring.
There is not a right way to do it, you should know what your users are expecting.