Firstly, deleting a user is an often unnecessary step, as similar results can be achieved by simply de-activating the user. De-activating a user stops the account from being used or adding towards your license limit, but keeps their work history intact.
Whichever way you want to go, explicit details for JIRA Studio can be found here:
You will need to be logged in as an administrator, and NOT have External User Management turned on. External User Management should be turned on when an other service is being used for user control; if you are using such a service you should use it to delete the user.
Some useful general information can be found here:
Just to keep this old answer current, there is an additional step in OnDemand to complete deactivating a user, detailed at the link below:
Hi Atlassian community, My name is Max and I work on the product integration team at Atlassian. I am pleased to announce the early access program for the Jira Cloud add-in for Outlook. This add-in...
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