A summary of how the mechanics work:
Direct Combat:Hostiles (and friendlies, in fact) are generated using an Army Strength system just like the Legions. One Army / Chapter / Fleet generates a combat dice - 1D10.
Any action taken by the unit uses the combat dice. In straight up combat you simply roll all the dice, apply all the modifiers, factor in Critical Hits, etc. and then apply the result.
For every ten points you win by, an enemy army is wiped out. Both sides then roll 1D10 for every ten points won by, 1D10 for every opposing unit that rolled a 1, plus an additional 1D10 for every Critical Hit their side scored and, finally, +1D10 if you rolled more 9's than your opponent in combat. If you beat the unit's combat value, you kill it.
Space Marines begin the Campaign with a combat value of 5, meaning a roll of 6+ is needed to kill them. However, as their armour improves and the Legions become ever stronger, this value increases. For example, (and I'll post this up so as to be fair to everyone.

) A Legion with Mk IV or Mk V armour only takes casualties on a 7+, and only on an 8+ once Mk VI rolls around.
"Attribute Tests":When a Chapter / Army / Whatever is seeking to gain recruits, fortify a position, raid enemy space or otherwise engage in something other than hitting a known, statted army block, they take an attribute test.
1D10 is rolled for each unit in the force, and the following applies:
1 - Failure.
2-3 - Poor result.
4-6 - Moderate result.
7-8 - Good result.
9 - Critical Result.
10 - Success.
It is up to the DM to decide what each of these categories means.
A roll of 9 is critical, and the DM should roll again on the table to determine what kind of critical it is. Further results of 9 result in 'compound criticals', which further up the ante. Should you score 2-3 Critical rolls in a row, then whatever follows should be something truly impressive... or disasterous, as the Dice Gods may see fit.
As with other rolls, Attribute Tests can be modified. A Chapter with +1 to all attack rolls, for example, should be given this bonus if they are seeking to attack hostile systems nearby. Note that in this case a roll of 1 is not always a failure; only Critical Failures are auto-fails. Thus, a suitably well-armed, well-trained and well-deployed force can be sent into a scenario where it could well succeed even with a roll of 1!

Space Marine Legions have an Armour Value of 6 at present. This increases as Power Armour technology advances.
Legion Strengths at the start of Turn 9 are:
Eagle Eye - Dark AngelsHomeworld: Caliban.
Legion Size: 10 Chapters.
Legion Traits:Librarius: +1 to one Army Group.
Intractible: +1 per Chapter in first round of combat. Cannot flee an engagement (All Chapters).
ShasOcho - Iron WarriorsHomeworld: Olympia.
Legion Size: 11 Chapters
Legion Traits:Aquilifiers - +1 to Combat Resolution (all Chapters).
Veterans - +1 to Combat for 1st Chapter.
Iron Armour: +1 to boarding style combat (Max 3 Chapters).
Primarch Traits:Veteran - +1 to Combat for Primarch.
Nobiliana - White ScarsHomeworld: Chogoris / Mundus Planus.
Legion Size: 13 Chapters
Legion Traits:Librarius: +1 to one Army Group.
Iron Armour: +1 to boarding style combat (Max 3 Chapters).
Primarch Traits:First Found - +1 Combat for all Chapters if Primarch is present.
Mkoll - Space WolvesHomeworld: Fenris.
Legion Size: 17 Great Companies.
Legion Traits:Veterans - +1 to Combat for 1st Great Company.
Leman Russ's Battletanks - One Army Group may be supported by Guard armour, granting +1 to combat.
Primarch Traits:We Don