Impeach the witness and attack their credibility by asking direct questions when you are afforded the opportunity to do so. Mind you, this is easier said than done. You should consider speaking with an attorney in person at a consultation in their office or conference room to discuss your case confidentially rather than on an open forum like AVVO or anywhere else for that matter.
Keep in mind that there are procedural Rules of Evidence you are expected to abide by when examining or cross examining a witness, Substantive Rules of Law you are expected to know if you wish to go forward as a pro se including knowledge of the pertinent Case Law in order to resolve your case favorably. Good luck.
Realistically, schedule a consultation with an attorney in person to get some meaningful guidance based on the facts and circumstances of your unique situation.
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Unfortunately, there is no good way to teach cross on the internet.
There is no 'pat' answer to your question--it all depends on the facts and circumstances of the case, the level of court, the rules of evidence/civil procedure, the credibility of the witness, YOUR capabilities and credibility in the case so far.
Best you can do is provide direct evidence that impeaches the witnesses testimony—which is a meaningless phrase if you’ve not done or at least studied it.
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I agree with my colleagues on the difficulty this question presents.
Where you are addressing inconsistent statements particularly, you really do need a record of those statements (either in a document like an email, or in a deposition or earlier testimony on the record.) Simply attacking a witness with an inconsistent statement because your memory is different is not going to be effective.
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