Is it ethical for a professor to get a graduate student to complete a manuscript peer review that the professor has been assigned?
Is it ethical to a professor to accept a manuscript for review, and then have a graduate student referee it?


Though commonplace in some fields (or among some professors), the practice of passing the review to a student, without the agreement of the editor, is utterly unethical for at least two reasons: 


The editor expects a review from that specific expert s/he required, not from a ghost one.
The work of the student would not be credited.


Moreover, in some cases, publishers ask to treat the manuscript as confidential, and in that case passing it to someone else can be considered as a breach of confidentiality.

The proper way to handle this passage is the following: the professor should write to the editor refusing the review and suggesting the student (or any other person) as a possible substitute, possibly outlining the credentials of this person to serve as reviewer. Then, the editor will decide what to do with this piece of information: either pass the review to the suggested reviewer or choose another reviewer.