What should a student do to correct spelling errors and punctuation in their written piece?

The best course of action for correcting spelling errors and punctuation in a written piece is to check the words that have been circled in a dictionary. This approach directly addresses the specific concern of spelling, as a dictionary is designed to provide correct spellings of words. It serves as a reliable reference tool for students to verify their spelling and ensure that they are using words accurately. By consulting a dictionary, students are able to identify and correct their errors independently, thus reinforcing their understanding and helping them to develop strong spelling skills.

The other choices do not focus specifically on spelling and punctuation. Returning to the desk to simply revise or add more information may not lead to fixing the errors present in the writing. While reviewing the piece with a friend can be beneficial for general feedback and clarity, it does not specifically target spelling and punctuation corrections, which is the primary issue presented in the question.