How do elemental shields work?

How strong are the cristallize shields and how does the type affect the damage?

Shields gained from picking up the Elemental Shards dropped by Crystallize reactions have shield health based on the level and Elemental Mastery of the character that triggered the reaction. These shields additionally have 250% effectiveness against elemental damage of the same element; in other words, they only take 40% as much damage when absorbing damage of their own element.

HP(Crystallize Shield) = HP(Base Crystallize Shield) * (1+%ElementalMastery-Bonus)

Base Crystallize Shield HP is only affected by the character level.

Character Level Base Shield HP
1 91
10 159
20 304
30 438
40 585
50 787
60 1030
70 1315
80 1597
90 1851

(Data for Version/1.6 - current Version/2.4)

Further increased by Elemental Mastery(EM) with the given formula:

444 * EM / (EM + 1400)

For further details, see Crystallize in Genshin Impact Wiki.

When the shield takes damage, the damage is scaled down based on the shield's elemental damage absorption bonuses and the active character's Shield Strength attribute.

DMG(Crystallize Shield) = DMG(Incoming) / (%ElementBonus * (1+%Shield Strength(Active Character)))
where %ElementBonus = 2.5(=250%) if Element(DMG) = Element(Shield), else 1(=100%)

If the damage exceeds the shield's health, the damage taken by character is the excess damage multiplied by the same shield bonus multipliers.

What happens if I pick up another shard?

Picking up a new shard simply replaces the old Cristallize-Shield with the new one. Only one cristallized shield may be active at a time. Multiple character shields may exist at the same time, just replacing itself (with Thoma as exception who may buff his own shield further). However, as stated by @SPArcheon in the comments, they take damage simultaneously.

Can I compare shields of different characters?

The shields of other characters such as Diona, Noelle and Zhongli simply got their own base HP and absorption. For a comparison of these, you can look up Shields/Comparison.

Credits go to Genshin Impact Fandom Wiki, where it's well explained in even further detail. All data for current Version 2.4.