I think you probably want to discuss it with whoever set up CLR for you, and find out more about the exact details of how it's configured. Normally with CLR set up it is not necessary to write the campaign ID to the contact record. Campaign membership is handled at a metadata level, not with actual contact fields.
The idea is that you're not supposed to have to worry about it. It should handle campaign membership properly (according to your CLR configuration) without you doing anything manually, other than setting the SFDC campaign id.
As for reading material, you probably want to read up on CLR in general. Here's a good starting point: Closed Loop Reporting Resources