When you cross-examine a witness
You want to emphasize evidence that is favorable to you
Sometimes, the testimony of the other side's witness helps your case. You can highlight the testimony that helps when you cross-examining the witness. In this case, you might ask the same, or almost the same question that the the other side used to get the evidence in the first place. The repetition of the evidence can help emphasize it and make it memorable to the judge.
You want to challenge the reliability of the witness or evidence
The most common way to challenge the reliability of the evidence is to show inconsistency between evidence produced during discovery and testimony provided at trial. If discovery before the trial generated different answers than testimony at the trial, it brings into question the reliability of the evidence.
In some cases, you can use cross-examination to show that the witness doesn't actually have sufficient first-hand knowledge of what happened. For example, if you are the defendant in a debt defense case, the likely witness for the plaintiff is a custodian of records for the original creditor. This person usually has detailed, personal knowledge of how the records of the business are kept. You could try to show that the witness doesn't actually have enough first-hand knowledge of the records to qualify as a custodian of records. You would do this by questioning the job duties of the witness to reveal that the witness lacks first-hand knowledge of how the records are entered, maintained, edited, safeguarded, etc. If you can do this, the judge could exclude the business records introduced from the evidence.
What you can about ask during cross-examination
When cross-examining the other side’s witness, you can only ask about the subjects that the plaintiff's attorney asked the witness about in direct examination. The legal term for this is the scope of direct examination.
If you need to ask questions beyond the topics of the other side’s direct examination, you need to call the witness as your own witness. Then you do your direct examination.
If you need to question the witness beyond the scope of direct examination, let the judge know. The judge might allow you to question the witness then. Or, the judge may tell the witness to stay for when it's your turn to present your case.
Tips for asking questions
When cross-examining a witness, you can ask leading questions or questions that suggest an answer. These questions are helpful because they can limit the range of answers that the witness can give and emphasizes points you want to make.
For example, the question, “It is not your job to enter data, is that correct?” requests an answer of “correct” or “incorrect,” rather than a more descriptive answer. This would be a good way to phrase a question to show that the witness’s job is not data entry.