How can I obtain a copy of my high school diploma?

Call or write to the school. They may want to see some proof of your ID.

If you're in a public school district in the U.S. contact the school district office. After graduation, schools forward cumulative records to the district office. They are scanned for the future and most store the paper copies for ten or more years. Old records are on microfilm and can be looked up and copies made.

Actually normally there is no way to replace the actual diploma unless you have just recently graduated,

The diploma is what you hang on the wall, there are many places that sell replica ones that can be used to get a copy of a real one. It is the transcripts that really prove you graduated and what grades you made. You obtain it by contacting the school you graduated from