How do I .... grant access permissions for SSIS to users?

SSIS access permissions are managed via Component Services. It is the DCOM object named MSDTSServer. Here are the steps to follow.

Component Services -> Computers -> My Computer -> DCOM Config -> MSDTSServer
Right click on MSDTSServer
Click properties
Click on the Security tab
Select Customize and add the users/groups to the Launch/Activation and Access tabs accordingly
Add the user to the local Distributed COM Users group
Restart the SSIS service