Let’s say I sue someone, for whatever reason: malpractice, breach of contract, libel, etc. In bringing evidence against them, am I bound by the same terms as the government is when gathering evidence in a criminal trial (e.g. the pesky Bill of Rights?) Or, am I free to introduce whatever evidence I can, as long as I can prove it is authentic (even if it was obtained in a manner that would be unconstitutional if the government did it)?
Short answer: You are not affected by the various amendments to the Constitution, other than to the extent that the court cannot allow you to do something during the proceedings that would deprive your opponent of life, liberty or property without “due process of the law.”
That last bit is the tricky part. In general, evidence you offer in civil trials in the United States will have to be admissible under a fairly complex set of rules, so complex, in fact, that lawyers take a course that lasts a whole year devoted to learning the ins and outs of several of the rules (for example, the rules on “hearsay” evidence).
And, of course, there may be laws that prohibit the method you choose (for example, wiretapping your opponent’s phones), which would impact whether or not the evidence will be admitted.
A more specific answer would require more specific facts about the type of evidence in question. 