As of 13/09/2020, this has been discontinued.
Linkart adds the Linker, a new item that you can use for cart linking, optionally, by default, consuming Chains. Carts have a frontal "locomotive" which dictates which direction they go in.
SHIFT + RIGHT CLICK to select the parent of a cart.
SHIFT + RIGHT CLICK again on another cart to mark it as a child of the parent.
LINKER is the item used for the previous actions. It can be disabled.
CHAIN is the item used by the LINKER for the previous actions. It can be disabled.
If the LINKER is enabled, and CHAIN is enabled, the player requires CHAIN in their inventory to link carts.
If the LINKER is enabled, and CHAIN is disabled, the player does not require CHAIN in their inventory to link carts.
If the LINKER is disabled, whether CHAIN is enabled or not does not matter. Cart linking can only be done by third-party mods that register a linking item.
Whenever the parent moves, the others follow - simple as that!