To add the module to your mission all you need to do is place the module Advanced Logistics into your mission, you do not need to sync anything to it. It uses an internal config file which can be altered either on a per mission or per mod basis.
Unfortunately the current logistics config for it in the CDLC is a bit empty, but Mike Force has a complete logistics config which can be used as a starting point for your mission, place the text from the link into your missions description.ext and it will allow you to pickup and load items into vehicles.
The Mike Force logistics config contains most of the static weapons and vehicles in the CDLC at the moment, and I'll be updating the default logistics config to match the Mike Force one soon.
The advanced logistics wiki page has been completed and will be available once the wiki is opened to the public, along with a link to the Mike Force config template as well.
You can then follow the wiki page for instructions on how to add more items from mods or others which are not already available in the config.