Tanking

EVE ships have two layers of defenses called shields and armor. The hull is not designed to absorb damage and is therefore not commonly employed as a defense option. Focusing on the shields and armor as damage absorbers, it is crucial to notice one main difference between them, namely recharge. I.e. the shields automatically recharge, without any action from the player while the armor gets 'dented’ and stays that way unless it is repaired.

Shields

Favoured by:: Caldari, Minmatar, some Gallente ships (Eos, Dominix, Myrmidon).
Variations:: Active Shield Tank, Passive Shield Tank
Modules used:: Shield Boosters, Shield Boost Amplifiers, Shield Extenders, Shield Flux Coils, Shield Hardeners, Shield Power Relays, Shield Rechargers, Shield Resistance Amplifiers, Shield Transporters (repair the target ship but don’t benefit the own ship).
Rigs used:: Screen Reinforcer Rigs, Core Defence Capacitor Safeguards, Core Defence Charge Economizers, Core Defence Field Extenders, Core Defence Field Purgers, Core Defence Operational Solidifiers. All rigs mentioned here have an increased signature radius as a drawback.
Drones used: Shield Maintenance Bots (repair the target ship but don’t benefit the owner).

The shields are the first line of defense when your ship starts to take damage. The beauty of shields is their natural recharge, which has to be overcome by the attacker before the total amount of shields left starts to go down. This can be used to the defender’s advantage by fitting modules that increase the shield recharge rate, thus increasing the amount of damage the attacker has to do before he starts to do decrease the total hitpoints of the shields. This is known as passive tanking.

The second method is the usage of a shield booster. That provides a quick restoration to the amount of shield hitpoints, say for one activation your shields, having fallen to 500 hitpoints from the 1000 total hitpoints because of an attack, can increase your hitpoints back to (for example) 700. The activation of this module costs you a certain amount of your ship's capacitor. Essentially one is morphing capacitor energy to shield hitpoints. And for increased effectiveness of the shield booster, one can fit one (or more) module of the Shield Boost Amplifier type, increasing the boost the shield boost provides, without increasing the capacitor usage. This is known as active tanking.

These two methods described are the only two ways to restore the total amount of hitpoints (by your ship) should you be under an attack and see your shield hitpoints slowly fizzle into thin space. A friend can have his Shield Transfer Arrays or Shield Transfer Drones active on your ship effectively providing you with an extra shield booster.

It is however quite possible to decrease the amount of damage that actually affects your shields, thus increasing the difficulty of bringing the total amount of hitpoints down to zero. Hardeners are the module type that does exactly that. What the hardeners do exactly is to allow your shields to be modified specially to resist one damagetype more effectively than the others. Thus you can fit a hardener that reinforces your shields' resistances to Thermal damage. If you are not satisfied with the results, you can simply fit another of those modules to your ship to further up the resistance. Then there are the hardeners that strengthen your shields against all types of damage; that type of hardeners does however not provide as good resistance as the more specific ones do, they only offer broader resistances (against all four types of damage, not only against one type of damage).

Two sub-types of hardeners exist, active hardeners and passive hardeners. Active hardeners use the ship's capacitor to ward against damage, thus morphing capacitor energy to damage resistance. Passive hardeners do not require capacitor energy to function, they simply function at all times. They do however not give as good resistances as the active hardeners do.

There is also the method of simply extending your shields' total hitpoints, in effect increasing the total amount of damage that has to be done to them before they no longer give your ship protection. That is by using a moduletype called Shield Extenders. They simply increase the capacity of the shield, so if you fit one your ship might go from having 10.000 shield hitpoints to have 12.000 shield hitpoints. That means the enemy has to concentrate more firepower to get through your shields or spend more time getting through them, both methods ensuring the increased probably of your enemy's destruction.

In existence are hundreds of combinations of the available modules to provide the best protection against enemy attack, the variations depending on ship types, ship sizes, the opponents and player preferences. Additionally there are ship modifications called Rigs available to do one of the thing mentioned above, provide increased recharge rate of your shields, provide boost to your shield booster and provide resistances to your shields. Additionally there are rigs that reduce the amount of capacitor energy your shield tank requires, thus increasing the time you can run your tank.

Armor

Favoured by:: Gallente, Amarr, Minmatar
Modules used:: Armor Hardeners, Armor Plates, Armor Repair Systems, Energized Plating, Resistance Plating, Remote Repair Systems (repair the target ship but don’t benefit the own ship).
Rigs used:: Anti-EM Pumps, Anti-Explosive Pumps, Anti-Kinetic Pumps, Anti-Thermal Pumps, Auxiliary Nano Pumps, Nanobot Accelerators, Trimark Armor Pumps. All rigs mentioned here have a decreased velocity as a drawback.
Drones used:: Armor Maintenance Bots (repair the target ship but don’t benefit the owner ship).

The armor is the second line of defense your ship has which will only receive damage once the shields have been completely over powered and no longer give any protection. The armor does not regenerate like the shields do, and thus requires an armor repairer to compensate for the damage taken. That is the only way to increase (by your ship) your armor's hitpoints should it go down when attacked. A friend can have his Remote Armor Repairers active on your ship or Armor repairing drones and thus effectively providing you with an extra armor repairer.

Like with shields, it is possible to fit resistance enhancing modules to decrease the amount of damage that actually affects your armor. And again, like with shields, there are two types of modules that allow you to accomplish that. Passive hardeners are the type that does not require capacitor energy to run and the active hardeners that require capacitor energy. Unlike shield hardeners there are two subtypes of passive hardeners called resistance plates and energized plates (often referred to as membranes). Active hardeners are however more simple category, containing only one variation which give added resistance to one type of damage. Identical to shield hardeners, the passive armor hardeners generally give less resistance bonus than the active hardeners.

There exists the possibility of increasing the total amount of armor hitpoints, just like with the shields, by adding an armor plate to your ship. Multiple plates can be added which in turn increase your total armor hitpoints accordingly. And again, you will ensure that it takes the enemy longer time to get through your defenses which increases the chance of you destroying him before he succeeds in overpowering you.

Similar to the shields and how they can be set up, there are hundreds of variations for armor defenses. Just like with the shields, there are ship Rigs that increase the effectiveness of your armor repairer by affecting the repair amount, repair duration or amount of capacitor energy required for one run. Additionally the rigs can affect directly one resistance type or the total amount of armor hitpoints, thus increasing the variations of possible setups. Depending on general design of the ship, such as the slot layout, distribution of durability and size all tribute to the different views and successes people have had in regards to specific setups. Both personal preferences, character's skills and in what type of gang you are flying in (should be not be soloing) affect whether you should go for this setup or that, shield tanking or armor tanking (or any tanking at all!).

Damage Control

One module is necessary to mention specially and in its own field. The Damage Control module (or a variant there of). That module requires almost no capacitor energy to run, but dramatically increases your shields', armor and hull resistances. This module alone guarantees you 10 - 15% resistances to both shields and armor, which obviously helps in any situation, whether you are tanking or not.

Other methods of 'tanking'

The word tanking there is in parentheses, because it has sort of left the original definition, or expanded it. Other methods include 'speed-tanking' which consists of simply traveling too fast for your attacker to hit you (his guns being unable to track you), 'EW - tanking' which consists of using Electronic warfare to prevent your opponent to get a weapons lock (or delay it by order of magnitudes), although this is often considered one type of an attack but not defense, 'cloak - tanking' which requires a Cloaking device and the skill (human skills) at using it effectively and cleverly, attacking your opponents 'out of the blue' and then disappear before they can react. There have also been talks about 'damage - tank' which simply is to destroy your enemy before he can do damage to you or get through your shields. But like was stated, these are sort of a 'meta' tanking techniques which is important to know about.