An operative must be within 1" horizontally and 3" vertically of terrain that's visible to them to climb it. Each climb costs a minimum of 2" movement (even if actual height is less).
An operative can only climb terrain within 3" vertically. If the terrain is higher than 3", the climb is not possible. The operative on the right cannot reach the top. The operative on the left is within 1" horizontally and 3" vertically of the wall, so they can climb.
An operative can climb a terrain more than 3" vertically if there's another terrain within its control range, similarly to when climbing a wall. Ladders are most natural for this, but another piece of terrain can also work, such as equipment barricades.
Each climb costs a minimum of 2" of movement, even if the actual height climbed is less. Here, the operative climbs only 1" of terrain but still spends 2" of movement on the climb. Note this is the vertical cost for the entire action, not for each climb.
When moving off terrain, operatives drop down. Ignore 2" of vertical drop per action. A 2" drop costs no movement. A 4" drop costs 2" of movement (4" - 2" ignored).
The 2" free drop is per ACTION, not per drop. If an operative drops multiple times in one action, only 2" total is ignored across all drops.