You can afflict elemental statuses when you deal damage with those elements, with the exception of Anemo and Geo, since they are mainly to interact with other elements, and also Dendro since it's not available yet (no character can apply it). When 2 elements combine, they will cause an elemental reaction.
You can see what element the enemy has, or what element affected you, by looking at the icons near the health bar. It's important to remember that even if the enemy looks like it's made of fire (like the regisvine bosses), if there is no fire icon, then it simply means that they are not on fire, and will not cause an elemental reaction when hit with another element. However, enemies have innate resistances to certain attacks, so it's still better to attack enemies with other elements instead.
Slime monsters are always pure element. So hitting them with another element will always cause an elemental reaction, and they are immune to their own element. You can use the slimes to practice and get to know elemental reactions with your characters.
Is a stat that you can increase with your gears. Increasing Elemental Mastery will only increase elemental reaction related damage. Characters like Lisa attacks with an element, but it still scales with attack, not elemental mastery.
You can check how much your Elemental Mastery boosts reaction damage by selecting "Details" below the status info when you go into the character screen.
Increases Charged Attack DMG by 35% if the character uses a Catalyst or Bow.
2 Types of Elemental Reaction
There are 2 different types of Elemental Reactions. 1 is considered "transfroming" and the other is "amplifying" (unofficial terms). Transforming reactions deals damage to an enemy, or have effects on them. Amplifying effects are mostly to deal increased damage, on the attack that activated the reaction.
The damage of transforming reactions are only based on a character's level, and elemental mastery of the character that activated the reaction, as well as the enemy's resistance. If you use Amber to deal Pyro damage on an enemy, then use Lisa to cause Overload, the damage of the Overload is based on Lisa's level and Elemental Mastery. If you use Xiangling's elemental skill to put down Guoba, and switch to Lisa and apply Electro first before the fire from Guoba, the Overload reaction's damage will be based on Xiangling's level and Elemental Mastery. Transforming reactions also can't crit.
Using Anemo on an enemy that has an element will cause a "swirl", removing the element on the target, and spreads it to nearby enemies. Since you can't apply Anemo element on to an enemy, this means that the Anemo characters will always be the trigger.
Geo element, when used on an enemy that has an elemental status on them, will remove that element and drop a crystal fragment. When picked up, it will give the player a shield of that element. Increasing your Elemental Mastery will only strengthen the shield value, not increasing your damage of the reaction.
Freeze and Shatter
Cryo (Ice) + Hydro (Water)
Freeze an enemy for a short period of time. You can still deal damage to them, and their defense will not increase. Attacking them with a heavy attack (Claymore, plunge attack, Geo element) will cause "Shatter," dealing physical damage that's based on level and Elemental Mastery.
Electro (Thunder) + Cryo (Ice)
Super conductor will deal damage in a small area, and reduce an enemy's defense by 40% for 8 seconds.
Electro (Thunder) + Hydro (Water)
Applying Hydro first, then Electro will deal Electro damage twice. Applying Electro first, then Hydro will deal Electro damage only once, but the two elements will stay on the enemy for a few seconds. Applying another element when both are still on the enemy can cause double elemental reaction.
Electro-charged is currently a buggy, and is expected to be fixed/changed in patch 1.1.
Electro (Thunder) + Pyro (Fire)
Deals Pyro damage in an area. This is the highest single reaction damage compared to the other transforming reactions.
Amplifying reaction damage just amplifies the damage that triggers the reaction. Unlike transforming reactions, the order in which you apply first, or second, actually matters. Amplifying reactions can also crit.
Pyro (Fire) + Hydro (Water)
This will cause an evaporation and removes the elemental status from the enemy.
Fire -> Water = x2 damage for the Water attack. Water -> Fire = x1.5 damage for the Fire attack.
Pyro (Fire) + Cryo (Ice)
Similar to Pyro and Hydro, this will cause an Evaporation, removing the elemental status from the enemy and they will take more damage from the last element used.
Ice -> Fire = x2 damage for the Fire attack. Fire -> Ice = x1.5 damage for the Ice attack.
There are currently no Dendro element characters, so there are no ways to apply a Dendro element to an enemy yet. It only exists from enemies with wooden shield, vines, or wooden boxes. You can only interact with them using Pyro. You can see the ones that you can interact with by using your vision (middle mouse button on pc).
Pyro (Fire) + Dendro (Wood)
When you use Pyro on anything Dendro related, it will cause continuous burning until it disappears, or extinguised using Hydro.
Mitachurls can extinguish the fire on his wooden shield if you put it on fire, unless you interrupt the animation.