You didn't mention the destination so I'll give answers to multiple scenarios.
If your target is another Server or Data Center instance, I've had luck with a Marketplace app such as Project Configurator. Note you have to have it installed on both (source and target) instances.
If your target is Cloud, you can use Jira Cloud Migration Assistant (JCMA) to export and import individual projects.
If your target is a different tool, you have to create a JQL query (project=X) to get all the issues and perform an export to CSV.
Hope this helps!
You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.