What you'll need:

• The more information you have on a particular filing or document the better, but usually a case name or docket number will suffice. One should also know in which court the document was filed.

Dockets:

• New Mexico Case Lookup allows users to search District Court and Appellate Court Dockets in New Mexico. However, it only provides a list of filings that cannot be downloaded. 
• Some State Court Dockets may be found in Westlaw and Lexis (Research | Content Type | Dockets). Docket coverage does not mean, however, that all filings within the coverage dates are held.
• National Center for State Courts offer links to public docket search engines for state and county courts when available on their Privacy/Public Access to Court Records webpage. 
• Also try searching for dockets on the court's web site.

Court Records & Documents:

• Some Briefs and Trial Court Documents may be available on Westlaw. Navigate to the case you're looking for and open the filings tab.
• Briefs, Pleadings and Motions may be found on LexisNexis. Either navigate to the "Briefs, Pleadings, & Motions" content tab on LexisNexis or use CourtLink. CourtLink Guide
• Some State Appellate Courts may make recordings of oral arguments and hearings available on their web sites.
• The Law Library's ILL Services, a library-to-library resource sharing service, does not order court materials that are held only by the court's clerk. Please contact the court directly for copies.
• If all else fails, you may need to reach out to the court directly and ask for help.