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Justia is a free site that provides limited access to select U.S District and U.S Court of Appeals Court dockets and filings. You can also try a quick Google search using the case name to locate court documents posted online.
For most state and local courts, you should check on the court website to identify the docket number of the case and see if any court docket/filings are available online. In most cases, you will need to contact the specific court to request specific court documents for your case.
A few additional resources require in person access to the Harvard Law Library. Check this Harvard Law Library site for information on hours and access policies for Harvard affiliates.