Dreadnought features two elements for reducing incoming damage: shields and armor.
Shields are the first line of defense and reduce damage before any armor or the hull is hit.
Damage that makes it through the shield is further reduced by armor and finally applied to the health stat of a ship.

Note to GSF players: There is no base damage reduction and there is no shield except you turn it on!

All ships have a tier-bound self-replenishing energy reservoir you may use actively for boosting speed, weapons or to turn on and power shields with.

In terms of armor there are modules out there temporarily increasing "damage resistance". And tier 3 or higher ships can equip officer briefings with small amounts of passive damage resistance.

Shields are vital for surviving in Dreadnought. And as shields consume energy, energy management is also vital.
Always keep a small amount of energy to turn on shields if taking heavy damage.

Shields block between 65% and 100% of the incoming damage.
So far only ramming other ships ignores shields (specific modules are needed for doing damage to other ships on collisions!).

Shield Usage
You turn on shields by pressing [F2].
Shields stay on as long as there is energy, or you actively turn energy usage off ([F4]).
Remember to turn off energy if you don't experience heavy fire anymore!

Beware of weapons that drain energy! Being hit by one of those might decrease or even completely drain your energy reserves.

Shield Stats
Shields behave differently depending on the ship class. You can find the shield stats in-game in the tech trees.

Dreadnought did implement shields having their energy consumption rates aligned to their damage reduction.
The higher the damage reduction the higher the energy consumption.

Rates by Class
Dreadnought65%very low
Artillery Cruisers80%medium
Tactical Cruisers85%high
Corvettes100%very high

Shield Penetration
Only modules for ramming other ships ignore shields.
There are no other weapons or direct damage modules reducing shield effectiveness or ignoring shields.
Though there are a lot of energy draining weapons and modules around. Beware!

Armor or "damage resistance" as the game calls the associated stat can be gained as passive permanent value through briefings and temporarily by modules.

Briefings and Modules
Starting with tier 3 the ships get access to officer briefings, which can tune ship stats dramatically.
The "101" named briefings don't have any dramatic effects, but some slight passive boosts.
One of those is Engineering 101, which gives the ship 6.5% passive damage resistance.

There is another officer briefing, Slow and Steady giving you an additional 10% damage resistance, but also reduces your base speed by 10%.

Besides briefings there are also modules that temporarily boost damage resistance.
Currently there are three: "Armor Booster Pulse", "Armor Amplifier" and "Armored Lockdown".

Armor Amplifier adds 80% to 99% damage resistance for a short amount of time.
Artillery cruisers have access to this module with super short durations of 2-3s starting with tier 4.
Dreadnoughts have access to this module with durations between 5-15s starting with tier 2.

Armor Booster Pulse adds 45% to 55% damage resistance to the ship itself and allies in up to 1.6km range for 5 to 8 seconds.
Dreadnoughts have access to this module starting at tier 4.

Armored Lockdown adds 95% damage resistance for 4 to 6 seconds depending on tier.
Only tactical cruisers have access to this module.
As with other "lockdown" modules all movement is stopped, and tier 3 and tier 4 versions also drain all energy if activated.

Armor Penetration
Dreadnoughts starting at tier 4 have access to a module called Armorbreaker Ammo, which reduces damage resistance by 50% (60% tier 5). This module is active for 5 seconds on tier 4 or 8 seconds on tier 5.
As far as I know by now the value is directly deducted from the damage resistance value of the target.

Purge beams and modules can reduce damage resistance. And of course, module disruption effects disable Armor Amplifier and Amored Lockdown. Armor Boost Pulse isn't affected, though this is considered a bug.

Defensive Stacking
Shield damage reduction and armor damage resistance do not add up!
The relation of shields and armor is multiplicative.
Incoming damage is first reduced by the shield rating. Left over damage is than reduced by armor.

Example: a dreadnought with shields up is hit by 1000 points of damage.
Dreadnought shields reduce damage by 65%. So, 350 points of damage get through the shields.
This dreadnought has no passive damage resistance but has tier 4 armor amplifier running, which is at 90%.
This means only 10% of those 350 get through to the hull, resulting in 35 points of damage.

While shields and armor don't add up, different armor components do add up!
This can lead to 100% of damage resistance or even more than 100%; though for only short amounts of time.