It is in fact a very broad question. Assuming you have a clear separation of application tiers (eg, using MVC), then this is the sort of stuff going in the business layer.
Taking your direct requirements, it could be fairly simple. In your users table, have a hasEdit, hasView, etc. For each item, attach a userid to it representing the creator. In the business layer, the rule is they have edit permission if they are the creator, or they have hasEdit = true.
Taking it up a notch, if you have different types, and the hasEdit permission is per-type, you need another entity for that.
userPermission
- userPermissionId
- userId (FK)
- typeId (FK)
- hasEdit (boolean)
- hasView
- etc..
To find out if they have permission to edit, you check if either they're the owner, or look up that items type and the current user in the userPermission table, and check hasEdit. You could make additional rules, like putting a global hasEdit in the user table. Or representing global hasEdit by an entry in userPermissionId with a NULL typeId.
This can get way more complex, using roles and variable numbers of permissions.. it all comes down to your requirements. You need to carefully spec out your business requirements (come up with a bunch of use cases), and then you can design from there. As is, there's really not enough information to come up with anymore than I've outlined here (and even this is probably not exactly what you need).