NOTE: Should be up to date as of U13, but don't expect the guide to be updated.
As Critical hits are even more powerful than before Helms Deep it's worth giving it some attention if you like to DPS on your Captain.
I've tried to give an overview of LtC Critical Hit mechanics here to make it easy to see how Captains can increase the number of critical hits and increase the critical damage magnitude to get the most damage out of the critical hits along with a couple of examples of how it can be put to use.
The overview is mostly for endgame as lower level Captains will not have access to many of the mentioned traits and bonuses.
Stats and Basics:
Critical hits have a base of 150% of max normal damage of the skill. A skill with 600-1000 normal damage will do 1500 damage on a critical hit.
Critical Magnitude is added to the 150%, as far as I know they're added additively so a 30% bonus to Critical Magnitude will make each critical hit do 180% of max normal damage.
Devastating Hits have a base of 200% of max normal damage of the skill. Critical Magnitude bonuses usually apply to Devastates as well but there might be exceptions.
Through critical rating it is possible to get 25% critical chance, 10% devastate chance and 36% (or more if you overcap) critical magnitude
Traits and Traitset bonuses:
React to Battle gives +5% critical chance for Devastating Blow, Pressing Attack and Routing Cry. It may also give +5% to Light of Elendil or Blade of Elendil?
Hardened Heart gives up to +30% critical damage magnitude when you are in Battle-hardened state (which you get after using Pressing Attack and/or Devastating Blow). Battle Hardened State can last from 10 to 20 seconds depending on legacies and HelmsDeep jewellery set bonus
Arterial Strikes gives up to 3% melee critical chance
Cutting Edge gives +30% critical damage magnitude for 7 seconds after using Cutting Attack
Vital Stroke gives up to +50% critical damage magnitude to Grave Wound Bleed ticks
Master of War (MoW) gives you and your blade-brother a buff whenever you (critically hit)/devastate with Inspire and Shadow's Lament. The buff gives a 100% chance to critically hit with your next damage skill.
MoW also gives you a Critical Chance (not rating!) for every hit you do while buffed by Standard of War. You get 1% Critical Chance per hit and it stacks up to 5 times.
Notable bonuses related to Critical Hits:
LtC initial bonus: Every critical hit gives +15% extra damage on your next melee hit
HoH trait Reversal gives +6% melee damage for 7 seconds after a critical hit
Devastating Blow has an inherent bonus to Critical Damage Magnitude
Blade of Elendil has an inherent bonus to Critical Chance
There is a +15% melee critical magnitude legacy for your mainhand weapon
A Captain with maxed critical rating (about 16,000 at lvl 95) can thus have 28% melee critical chance and 36%+ critical magnitude (51%+ with legacy) so even at the start your critical hits will be doing about double damage of a normal hit and give +15% damage on the next melee hit, making critical hits really useful.
However, it is first when you start combining the stats with the other bonuses that it starts to become really powerful.
Building the Damage, Critical Strike chance and Magnitude:
1. Preparation before battle: You can start out with Time of Need, To Arms and/or Standard of War to increase your damage. If you use Time of Need, using Routing Cry right away for the -15% attack duration buff is a good idea. It is a really good idea to use Standard of War now rather than later in your rotation so you have the full +5% Critical Chance buff as soon as possible.
2. Building Critical Magnitude: Use Battle-shout + Sure Strike (for Relentless), then Devastating Blow/Pressing Attack to get Battle-Hardened for the +30% critical magnitude. Don't use Blade of Elendil as it will consume Battle-hardened. Then I suggest you use Cutting Attack for the 7 second +30% critical magnitude.
3. Getting MoW buff: You can then use Inspire and Shadow's Lament in hope of critical hits. if Inspire crits and you get MoW bonus, using Shadow's Lament will consume the buff, critically hit and give you the MoW bonus again. Not only does this potentially give you a lot of damage from Shadow's Lament if it crits, but the chance that you have Master of War critical hit bonus after Inspire+SL is about 50% if you have 28% critical hit chance.
(MATH: the chance of not critting with Inspire is 72%, the chance of not critting with SL is 72%, 0,72*0,72 = 0,52, so there's 52% risk of not critting with either Inspire or SL. I'm not sure how Devastate Chance is added in, but that still further increases the chance of getting the MoW buff. The 1-5% Critical Chance from Standard of War MoW bonus increases the chance even further.)
Using the MoW Critical Buff:
After the building phase you hopefully have most/all of the following buffs:
MoW 100% critical chance on next skill
Cutting Attack +30% critical magnitude (though probably only with 1-3s duration left on it)
Battle-hardened +30% critical magnitude (though probably only with 1-13s duration left on it)
+15% damage on next melee skill from LtC initial bonus (from SL crit)
+25% damage from To Arms
+20% damage from Time of Need
+30% damage from Standard of War
Relentless buff from Sure Strike
5% Critical chance from Standard of War + MoW buff
I suggest using one of the following skills depending on your goal:
Single Target Burst: Devastating Blow. The Inherent Critical Magnitude makes this skill crit really hard with direct damage.
3-6 target AoE Burst: Pressing Attack. If you use the MoW crit bonus on Pressing Attack, both of the attacks will critically hit on all your targets (normally the first attack never/rarely crits)
6+ target burst: Standard of War. It does not do that much damage but it has an unlimited amount of targets within its radius, so against a large number of mobs close to eachother this attack can do a lot of damage.
Single Target Damage over Time: Grave Wound. Grave Wound does not do that much damage by itself, but by having Bleed damage legacy on your mainhand (+40% damage) the bleed can be quite potent. The MoW crit buff make every bleed tick critically hit, and the Vital Stroke trait gives the Grave Wound bleed +50% critical magnitude. That makes it possible for Grave Wound bleed to tick for 2000-3000 damage every 2 seconds. The bleeds from Grave Wound also seems to stack, making Bleed Pulses legacy worth considering.
AoE Damage over Time: Grave Wound. This is where Grave Wound can become your main DPS source. As described in Single Target the bleed can become very powerful, and if you use Grave Wound on a target that has the Cutting Attack bleed on, the Grave Wound Bleed will also be applied to all nearby enemies (about same radius as Standard of War). In some situations that can easily become 10+ targets bleeding for 2000-3000 damage every 2 seconds for the duration of Grave Wound.
Hopefully this gives some inspiration as how to make use of the LtC mechanics If I made any errors or forgot relevant mechanics do please comment.