Connector for Salesforce & Jira works with Jira Service Desk out of the box.
However, due to a known bug in Jira Service Desk, an extra permission configuration may be required to make it work. This bug most likely affects Jira Service Desk projects created prior to August 2016.
If your instance is affected, see Configuring Project Permissions for Project Role. The guide assumes that you have installed Connector for Salesforce & Jira.
Connector for Salesforce & Jira does not currently work with the Jira Service Desk comment visibility setting.
If you have not installed the Salesforce package, go to Installing the Salesforce Package for Salesforce & Jira Cloud Connector.
Otherwise, view Setting up a connection to Salesforce.