Providing details of all general Do’s and Don’ts in cross-examination is beyond the scope of this Forum, on which basically specific questions of law concerning a particular user are replied to. You may perhaps get plenty of resources if you search it on Internet.
However, let me answer your specific questions.
Firstly, please appreciate that in Section 146 of the Evidence Act, it is clearly laid down that during cross-examination of a witness, his veracity may be tested and his credit may be shaken by injuring his character:
“146. Questions lawful in cross-examination.—When a witness is cross-examined, he may, in addition to the questions hereinbefore referred to, be asked any questions which tend—
(1) to test his veracity,
(2) to discover who he is and what is his position in life, or
(3) to shake his credit, by injuring his character, although the answer to such questions might tend directly or indirectly to criminate him, or might expose or tend directly or indirectly to expose him to a penalty or forfeiture:
Provided that in a prosecution for an offence under Section 376, Section 376-A, Section 376-AB, Section 376-B, Section 376-C, Section 376-D, Section 376-DA, Section 376-DB or Section 376-E of the Indian Penal Code (45 of 1860) or for attempt to commit any such offence, where the question of consent is an issue, it shall not be permissible to adduce evidence or to put questions in the cross-examination of the victim as to the general immoral character, or previous sexual experience, of such victim with any person for proving such consent or the quality of consent.”
So, yes, if a witness is making a false statement about his education, you can discredit him in cross-examination by showing that he is lying about it. This can be done in both ways mentioned by you, i.e., by bringing in evidence a new document in evidence during cross-examination to show that he stated falsely, or to use an evidence already existing before the court to discredit him (you can refer to that document, already on record, and question that witness).
It is always advisable to discredit the witness during the cross-examination itself by relevant evidence. He should be asked about such evidence which can shake his credibility.
Of course, you may also have to highlight this issue during the final arguments to show to the court that such witness is not reliable.
Dr. Ashok Dhamija is a New Delhi based Supreme Court Advocate and author of law books. Read more about him by clicking here. List of his Forum Replies. List of his other articles. List of his Quora Answers. List of his YouTube Videos.