Trial courts issue orders (granting a divorce, sentencing a defendant to jail, etc.), not opinions with precedential value. Traditionally the only way to get state trial court opinions was to go to the courthouse but now some are available online.
Trial court decisions are reviewed by intermediate appellate courts (Courts of Appeal or Circuit Courts) which issue opinions that are precedent for trial courts. The party who loses at the trial level may appeal the outcome by arguing that the trial court erred on an issue of law.
Court opinions are available from some court websites, from PACER (public access to court records), and from many free and paid databases, and in print.