Damage Reduction

Damage reduction works is as follows:

If an attack does N damage, you take N reduced by Armour (calculated by adding your Strength to your Armour from gear)
reduced by resist to that particular damage type (resistance rating is calculated by adding 1/10th of your Intelligence to your resists from gear, both general and specific to that type to get a rating and then compared to monster level. It claims to be a percentage but it isn't)
reduced by 30% if Barbarian or Monk
reduced by special damage reduction affix if appropriate, for example the 10-20% melee damage reduction on the String of Ears legendary belt
reduced by any skills or passives (eg Witch Doctor's Bad Medicine)

Then it rolls your chance to block. If a block is generated your Block Amount is subtracted from the modified damage.

At some point it rolls your chance to dodge. (It doesn't matter at what point in the process). If successful no damage is taken from this attack.

Some notes:

- damage reduction from Armour and Resists is for same level opponents. This means that everything in Inferno reduces your listed damage reduction from Armour and Resists. You are getting less than the amount displayed on the character sheet.

- the field Damage Reduction displayed on the detailed character sheet is damage reduction from Armour only. It's always the same value as what you see if you mouseover your armour with detailed tooltips displayed.

- for softcore all damage reduction is more or less equally valuable. (That's arguable). In hardcore you should probably plan around worst case scenarios. So dodge is a less useful stat because you really need enough effective health to survive when you roll snake eyes on your dodging. Armour, resists and vitality will tend to perform the same in any situation where you're taking damage but dodge will vary. You may get lucky some fights and unlucky in others. Same to some extent for block - in hardcore you probably have to plan around getting hit several times while not rolling a successful block or dodge. This is pretty much the same philosophy as WoW tanks use and there's a lot of good theory written about effective health tanking. The motivations are pretty similar - a WoW tank doesn't want to roll snake eyes and wipe his raid and a hc D3 player doesn't want to roll snake eyes and have to start over.
This is important because there is a lot of advice for Barbarians in particular to gear up with Stormshield and Justice Lanterns which is perfectly decent advice for softcore but may not be the best strategy for hardcore.

- for all that all damage reduction is good and dodge seems to be very underrated in softcore. You can get a lot of dodge very cheaply when your dex is low. Even in hardcore it doesn't hurt to be lucky.

- generally speaking defensive stats aren't on true diminishing returns. Sure, it takes the same amount to improve from 90 to 91 as it did to go from 0 to 10 but both of those are a reduction of 10% damage taken. In other words the returns diminish for the number displayed on the character sheet (which is cosmetic) but don't diminish for the amount of damage you take (which is what kills you). The exception is Dexterity. Dexterity gives less dodge per point the more you have of it.
- Vitality is an alternative stat for survival. In many ways it's less good than any other way of generating the same amount of effective health. I'd rather have 75% damage reduction and 20k life than 50% damage reduction and 40k life because most healing is a fixed number and a 10k heal makes a bigger splash in a 20k health pool. On the other hand Vitality gives a LOT of effective health.

- there's an effective health calculator for most classes here

- the Enchantress gives a 15% armour buff that is up just about all the time.