Imagine a chainlift like in a rollercoaster - a chain which moves from a to be and a hook can snap into it.
This is basically how this chainlift works. 
The whole system is based on Waypoints and Movers, The hooks which will hook into the path between two waypoints.
Waypoints can be linked with Routes which you can only switch if you got Wiremod installed.
You hook up a Mover by just moving it between two linked Waypoints.
Also there is checkbox called 'Waypoint picks up Movers' which will reset after every spawned/modified Waypoint. Movers will just hook up if the Waypoint in beginning of the Route segment you try to hook up the Mover got this enabled - for performance reasons.
If hooked up the Mover will move to the next Waypoint if it reaches it it will move to the next Waypoint or if the Waypoint is not linked to another Waypoint it will just leave the whole Track system and Havok kicks in making it move like every other prop.
By default Movers will just take Route 1 so make sure you use Route 1 if you won't switch the route.
About the speed the Mover will move - It's defined by the addition of Mover Speed (next) Waypoint Speed and the Max Speed Fraction all of those 'Speed's are values and have nothing to do with the speed the Waypoints move or something ;P

So about that Max Speed Fraction it's basically the fraction of the current route semgent the Mover has to pass to reach it's max speed (max speed = speed of mover + speed of next waypoint).
So if set to 1 it will reach the max speed at the other waypoint, if it's set to 0 it will instantly switch to max speed when it passes the wapoint, set it to 0.5 and it reaches max speed right in the middle of last and next waypoint - you get the idea ... hopefully.

Both Waypoints and Movers got Wiremod Inputs
Waypoints:
Route: Sets which route Movers should use. (If there is no route to that input mover will just hook out.)
Status: Sets the status of the Waypoint 0 = Default Mode; 1 = All Movers will stop at that Waypoint; 2 = All Movers will hook out;
Movers: 
Hook Out: Will hook out the Mover from the current route
Speedmod: Multiplies the Speed by it's input

So far about the whole system now how to use it

Reload to switch between spawning / linking

If you're spawning: 
Left Click to spawn or update a Waypoint 
Right Click to spawn or update a Mover

If you're linking 
Left Click to select a Waypoint

If you selected a Waypoint
Left Click to set target
Right Click to deselect

Sprint + Reload to switch enable/disable automatic Waypoint linking

Automatic Waypoint linking allows you to automatically setup a route between new spawned Waypoints.
If you then build up a route by just spawning Waypoints you can finish it by either disabling the automatic Waypoint linking, Click on the last spawned Waypoint again or by clicking another Waypoint and it will hook up to that one.
If you want to start a route at an already existing Waypoint just aim at it and then enable the automatic Waypoint linking.

So far about how to use it now I'll explain what the single context menu values do:

Hook Up Mover: Enable or Disable hooking up Movers at the next spawned or updated Waypoint (just enable hooking up at the really needed waypoints)

Waypoint Speed: The Speed the Waypoint adds to the Moverspeed - can be both positive and negative

Waypoint Route: Sets the Route you're gonna set by either auto linking or manual linking

Max Speed Fraction: Sets the Max Speed Fraction of the Waypoint

Mover Speed: Sets the speed of the Mover

Mover Mass: Sets the mass of the Mover - The more mass the more powerful it is.

Spawn Frozen + Spawn Welded:  I don't think I have to explain those.