There's lots of ways to do it, but I'd strongly recommend using add-ons.
What exactly are you trying to synchronize? If it is issues and its fields, take a look at ConnectAll.
As Nic said there are a lot of ways to do this - please provide some more details about what exactly do you want to sync.
Here's one product by iDalko that allows syncing issues between instances
http://www.exalate.com/
https://marketplace.atlassian.com/plugins/com.exalate.jiranode/server/overview
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