When installing java, if using the official Oracle version, you can get a manual download so you don't run into network problems while its installing. A link is on the page where you can click "install java", but it's easily missed. Visit the manual download page here:
https://java.com/en/download/manual.jsp Make sure to grab the proper version for your operating system. (Note that 32-bit versions are still available. Odds are you want the 64 bit, which is not what is served up by default by the web installer.) You may also have some security software of some sort that may be blocking Java from installing.
Once Java is installed, you can open a command line and type the command "java -version" and get something like
java version "1.8.0_281"
Java(TM) SE Runtime Environment (build 1.8.0_281-b09)
Java HotSpot(TM) 64-Bit Server VM (build 25.281-b09, mixed mode)
After that, click the play button, save the file to your desktop or another convenient location, and it should launch with a double click.
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