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The Notice requirements (not including any local requirements) is found in Fed. R. Civ. Proc. 26. In layperson terms, you have an affirmative duty to provide certain information to the other parties to the case, or you could be subject to sanction by the court.
Hope this helps.
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You're opening up a huge bag of worms, generally called the "tools of discovery," which are found in Fed. R. Civ. Proc. Rules 26 through 37 and 45. If you require additional discovery, then you can use, among other things, a request for interrogatories, request for production of documents and other things, a notice of deposition, of a party a subpoena for deposition of a nonparty, and a request for admissions.
Which tool to use depends on what you're trying to discover, sometimes more than one tool is preferred -- other times, no tool other than to bring a witness to trial will do.
If you want more info concerning discovery, then you'll have to visit a local law library, or alternatively, pull out your credit card and purchase:
Federal Civil Procedure Before Trial, 5th Circuit Edition
Federal Civil Trials and Evidence
Bankruptcy, National Edition