Movement Phase

Moving
The Movement Phase comprises of four steps that are followed in strict order:
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Declare Charges
If you want any of your troops to charge into Hand-to-Hand Combat, you must declare this before any units are moved or measuring takes place.
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Compulsory Moves
Move any units that are subject to a compulsary movement rule—such as vehicles moving out of control.
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Move Chargers
Move any units that were nominated to charge in the first step.
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Normal Moves
Move any other units.
Declaring Charges
To engage an enemy unit in Hand-to-Hand Combat by charging it, the intention must be declared at the very start of the Movement Phase. To declare a charge, each model—or group of models—in the attacking unit nominates a target for its charge. Models from the charging unit do not all have to declare against the same enemy unit, provided this does not contravene any other rules for charging.
The attacking player must be reasonably confident that the charging unit can reach its target; however, the distance may not be measured before declaring the charge. Charging troops must have a clear run at their target—they cannot charge through other models, and any terrain features should be taken into account.
Once a unit has been declared as charging, it may not participate in the Shooting Phase, even if it fails the charge.
Compulsory Moves
There are occasions when a model may be forced to move irrespective of a player's wishes—these are Compulsory Moves. Common examples are vehicles that go Out of Control or models that become Frenzied, but numerous rules can trigger such moves. Compulsory Moves always occur before planned—or Normal Moves—which can lead to all sorts of chaos.
Charging
The purpose of Charging is to move models into Hand-to-Hand Combat—a model cannot engage another model in Hand-to-Hand Combat without charging. A whole squad must charge together and can travel up to double its normal Movement. Each charging model must attempt to engage the nearest enemy model, but may choose to ignore models already in Hand-to-Hand Combat. If, because of Compulsory Moves, another enemy model is closer than the charging model's originally declared target, the charging model must target the nearer model instead.
A charge is considered successful if the charging model can achieve base-to-base contact with an enemy model. If the enemy model is behind cover—such as a wall—the charging model must reach base-to-base contact with that instead. If no enemy model can be reached, the charger moves its full charge distance, stops, and may do nothing else for the rest of the turn. Models may be charged even if they are in Hiding.
Normal Moves
Models can move up to their Movement rate in any direction. Not all models in a unit are required to move, provided Squad Coherency is maintained; for example, you may reposition part of a squad while leaving a model with a Move or Fire weapon stationary, allowing it to still shoot. Eligible models may also Going into Hiding.
Preparing Overwatch
If a unit has not Charged or made a Compulsory Move, it may forgo its turn and instead prepare Overwatch—while preparing Overwatch, models may change their firing arc by turning, but may not otherwise move. All models in a unit must enter Overwatch together. A unit on Overwatch does nothing for the rest of its turn, but may shoot at any time during the opponent's turn†—this lasts until the beginning of the unit's next turn.
† In the original rulebook, Overwatch shots were only permitted during the opponent's Movement Phase; this was later revised in a White Dwarf Q&A.
Terrain
If an obstacle has a gate, the gate is assumed to be open unless otherwise agreed, and troops may pass through as if it were open terrain.
The penalties for Difficult Terrain types and obstacles are cumulative.
Not all ground is equally easy to cross. To represent this on the tabletop, there are four types of terrain, each with an associated movement penalty:
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Open Terrain
No penalty—brush, scrub, woods, debris, ruins, boulders, crevasses, stairs, ramps, steps.
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Difficult Terrain
Cross at half Movement—steep slopes, thick forests, streams, shallow water, marshes, soft sand, ladders.
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Very Difficult Terrain
Cross at quarter Movement—almost sheer slopes, tar pits, swamps, pools, fast flowing rivers.
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Impassible Terrain
Cannot be crossed—deep rivers, lakes, sheer cliffs, very high walls.
Obstacles
Obstacles no more than 1" high and/or 1" broad may be moved over without penalty. If an obstacle is taller than 1" but no more than twice the height of the model attempting to cross it, the model may use half of its Movement to do so. When an obstacle is more than twice the height of a model, it counts as Impassable Terrain for that model.
If an obstacle has a gate, the gate is assumed to be open unless otherwise agreed, and troops may pass through as if it were open terrain.
The penalties for Difficult Terrain types and obstacles are cumulative.
Running
Running allows models to double their normal Movement. All models in a squad must run together and if they do so they cannot fire their weapons during the Shooting Phase.
In the original rulebook, the following also applied to the rules for Running:
If running troops move to within 8" of enemy troops then they immediately halt and ready their weapons.
—Warhammer 40,000 Rulebook (2nd Edition)
It is highly recommended that you disregard this, as it breaks the game. Olden Demon, on YouTube, explains how here.