Troops move 6 inches or 2d6 (take the highest) when in difficult terrain (trees, ruins, etc...)
Vehicles can move 6 inches and fire one main (STR 5+) and all defensive weapons (STR 4 or less). Optionally, they can move up to 12" and fire nothing. Not moving allows them to fire everything.
Fast Vehicles basically get to add 6" to both rules.
The equation: 7 - Ballistic skill (BS is how it shows on the unit statline) is the number needed to hit. Easy to remember. So a BS of 4 hits on a roll of 7-4=3.
Each units members fire simultaneously and at the same target. Not all must fire.
To hit you must have line of sight LITERALLY from the eyes of the firing model to the target. EACH models eyes are gauged this way, so it is possible that some will see the target as obscured (or not at all) and others in the same unit will have a clear line of sight.
Each individual weapon that is in range may fire. Rapid Fire weapons are reduced to 12" range if you move. Rapid fire weapons can always fire 2 times at 12" range, moving or not.
Once you roll to hit, dont count the dice. Waste of time. Just take out all the misses (good ettiquette). In our example, 1's and 2's miss. Then pick them up and roll the remaining dice to wound. Wounding uses a chart you must use or memorize. Put in simplest terms, a weapon of equal str compared to the tougness of the target will wound on 4's. It goes one step the other way depending on the tougness comparison. So a STR 5 attack vs. tough 4 means you need 3's (one step removed from equal) to wound. If it is against tough 5, you need a 4 and so on.
Hand the dice that wounded to the opponent and have them roll their saving throws (saves so much time). They only get a saving throw if the AP rating of the weapon is not equal to, or lower than, their saving throw. For example, a 3+ armor saving throw will be trumped by an AP 3,2 or 1 weapon (AP is listed with the weapon description at the back of most Army Books). Low AP ratings are good. Lets assume the weapon AP is 4 and therefore does not trump the armor save. In this example, they would cast the dice you handed them and any 1's or 2's represent wounds actually taken. The person losing the models gets to choose which ones die. See the rulebook for rules on allocating wounds. In short form, each pool of models in a unit that are the same in game terms get allocated wounds as a pool. So for example if you do 9 wounds to a unit that contains 4 A's and 4 B's, you'd have to give 4 to the A's, 4 to the B's and then decide whether the A's or the B's will take the final wound. Then roll your saves. If only 4 wounds, you could split them up either way because there aren't enough to FORCE you to spill over into the other unit. Just make sure everyone takes a wound before you assign a second round of wounds to any one pool.
If you shoose not to shoot you may substitute shooting for a D6" move that is not slowed by terrain (but dangerous terrain may still wound you. Roll for each individual model. On a 1, that model dies when moving through Dangerous Terrain)
Vehicles have armor ranging from 10-14. When you shoot a weapon and hit a vehicle, you then roll a D6, adding the Weapons STR. So a heavy bolter is STR 5. If you roll a D6, and get 6, your total is 11. that is the armor you are able to affect with that shot. If the value is equal to the enemy armor, you glanced it. If it exceeds the enemy armor, you Penetrated it. In both cases you roll to see what happens, using another D6. See page 67 for some rules on that. there is an easy to read chart for this in the very rear of the main rulebook. Learn it. Know it. Love it.
After all units have shot and resolved the deaths of many, it's almost time for assaults.
Normal units assault 6" or else 2d6 inches (take the best of the two) when moving through difficult or Dangerous terrain. Beasts/Cavalry charge 12" instead. Generally the order of this movement is as follows:
1. Closest model must make a DIRECT line to the nearest enemy model in the unit.
2. Independent characters move next.
3. Every model must attemt to get in base with a model that isn't already engaged if possible.
4. Once all the models have been moved that can get into base, move the ones who cannot as close as they can possibly get.
5. If you miss the charge, nothing moves at all. I know. I know. Just accept it.
Once this is done the enemy you charged does the same exact thing except step 1.
Finish moving all chargers before moving on.
Then dice are chucked.
close combat happens in strict initiative order. Init 10 models go first and then so on until you are done with the INIT 1 models. Easy enough.
Each model gets its Attack characteristic in dice to roll, plus 1 per model when charging, +1 per modl that also has a pistol+close combat weapon(CCW) or just two CCW's. Any power weapons should use a different colored die so its clear which are which.
To hit is a chart you can memorize, but in short form: if the enemy Weapon Skill(WS) is lower than yours, you need 3+ to hit. simple.
If they are equal to or better than your WS, then you need 4's.
On rare occassions, you may need a higher number if the difference between your skills is vast enough. generally this is when the opposing weapon skill is 2x+1 your WS. Tau have WS 2, so any time they try to hit a WS 5 person, they need a 5+ because 5 is 2x+1 their weaponskill.
Like shooting, roll the number of dice, dont count them, get rid of the misses, then roll them again to wound (same chart as shooting to wound) and give those dice to the opponent to allocate to their men. Unless it's a power attack, they will always get their Saving throw. their is no AP in close combat.
This happens at each initiative count. so its possible to have half the unit attack on init count 5, and the other half on init 4.
Once both sides are done figuring out who died, compare the number of wounds done (not models) and then the winner is the one with the most. Some wargear can increase this number artificially. If tied, you both move in closer (up to 6 inches) following the rules before so that everyone stays engaged.
If someone did more wounds, the enemy must roll 2D6 and the target is the units highest leadership score. Every losing unit involved must roll. There is a modifier to this equal to how many wounds you lost by. So an LD 9 unit that lost by 4 would need a 5 in order to stand their ground. if they do, treat it like a tie. if they dont, they run.
When they run: the running unit rolls a D6 and so does the enemy winner. Add your init score to the roll. if the enemy equals the total of the running unit, the running unit is cut down mercilessly and removed. Finit. If the losers exceed the enemies total, they run 2D6 inches towards the long board edge they originally deployed from.
And that's pretty much Warhammer 40K in like 1 page. hehehehe.
I've obviously left a few things out that are specific to a lot of weapons and vehicle types and all that but this is the basic mechanic.
Tactically, there's a lot to how you use units and time them. Strategically there are a lot of plans you can implement as an overarching battle plan. thats the fun of the game and takes a LOT more time to really get down. You'll learn that through hard won experience.
I hope this helps. Good luck.