Custom permission sets can be easily made. Typically a custom permission set is going to go with a custom Role, in fact, once you create a custom role, you're given a link that goes directly to the permission set for that role.
So, to keep it simple, you'll want to be at Admin menu > User management > Roles. From the Roles panel, do the following:
Click on the edit permissions link respective to the role you're interested in adding a custom permission set to
Select the permissions you wish to grant to this role. Remember, this is up to you as the administrator. Pay special attention to notes next to the permissions that say things such as "give to a trusted role only" - typically this means that this permission can cause problems on your site if used by someone maliciously, or even accidentally. There are many, many permissions to go through, consider them carefully, but remember that you can always return and change them as needed.
Once all of the permissions have been checked, scroll down to the very bottom of the panel and click the Save permissions button.
Your custom role and permission set are now complete!
Now you just have to assign the role to a person on your site...