Research the new type of wagon, then build them as part of a train.
Add at least one station to the train's schedule, then open one of the wagons; you'll see the logistic configuration on the left side of the screen. (If you're using LTN for your deliveries, explicit configuration isn't needed - the wagons will detect what items they're loading or unloading from the LTN dispatcher.)
Set which items you'd like the wagon to request and provide at each specific station. When the train stops at each station, the logistic wagon will request or actively provide to the logistic network - buffer chests at the train stop work great for both loading and unloading rapidly.
When you've finished setting what to request and provide at each stop, you can copy all settings from the wagon to all others in the train via the button at the bottom of the window, or by doing a copy-paste between wagons (shift-right click to copy, shift-left click to paste).
Translations and other contributions are welcome, preferably through GitHub.
Caveats/Known Issues:
- Cargo door animation doesn't show the doors being opened if the wagon's on a curve or diagonal. This is cosmetic only; the logistic wagons work just fine when stopped on curves.
- Due to the way the mod uses a proxy player entity for requests, it's possible to request more than will fit in a wagon, especially if you use cargo filtering. If you request too many items, the extras will be dropped on the ground and marked for deconstruction by robots when the train leaves the station or is switched into manual mode.