Realize that courts do not keep some documents, like police reports, even though they might be used in court cases. You need to know who the official "keeper of the record" is for the document you want. Most documents (like evidence photos) generated in a police department are legally maintained by that department and you can obtain them using "discovery" requests or open records requests. If it's a decision, decree or judgment you're after, the court that made it is the keeper and if you want a trial transcript, most courts will provide them for appeals for a nominal fee.
Know that if you need something like a divorce decree, the register of deeds may be the keeper of the record. Divorces, marriages and deaths are often kept by county clerks who maintain websites where you can order certified copies.
Check with the clerk of court to see if the court is the keeper of the record you want. Be sure to know what it is that you need--the title of the document. If it was issued on a certain day or as part of a certain case, have that information, too. Most clerks are very helpful but if there is hesitancy to produce a record, make a formal, written public records request for the material.
Be aware that the simplest document to retrieve is a notice or summons that has been filed that you've lost. If it's just a matter of finding out where and when you're supposed top show up, ask the clerk for a duplicate. Most clerks of court will happily find what you want or tell you who's responsible for that record. They are absolutely forbidden, however, to give legal advice.
Know that information on the federal Freedom of Information Act of 1996 and Privacy Act of 1974 is available on the US Department of Justice's website as well as a number of other sites. State Open Records laws are part of state statutes and are often available on websites maintained by bar and press associations, state attorneys general and journalism schools. Search "open records" and the name of your state.