First some Google Analytics terms:
- Campaigns - The source of paid traffic (such as PPC).
- Goals - Conversion events
To get Google Analytics to attribute conversions to your PPC traffic you need to configure Google Analytics for both campaigns and goals.
Use the Google Analytics URL builder to build inbound URLs for all your paid traffic. "Tagging" your landing URLs with the parameters that analytics knows about will cause that traffic to get reported under "Acquisition -> Campaigns".
Set up each conversion as a "goal". Goals can be triggered when a user visits a specific URL (such as "checkout complete"), or more fine grained if you ping Google Analytics with "events" when a user converts.
After you have done the setup, analytics will show you how your campaign traffic is performing. It will not let you see the traffic source for any individual user. It is against the Google Analytics terms of service to use Google Analytics to track an individual user. Only aggregate tracking is permitted.
If you want to know for any given conversion the source of that user, you will have to track it yourself outside of Google Analytics. I've done this before by storing source in the user session (when the user lands) and then on conversion, setting this source into the data of the conversion.