What is Spellburst in Hearthstone?
Hearthstone has many card effects that are common enough that they get their own keyword - a word or two that immediately tells you how the card works. Let's take a look at the Spellburst keyword.
A one-time effect after you cast a spell.
Spellburst is a keyword introduced in Scholomance Academy. While you control a Spellburst minion, it has a special effect that triggers the first time you cast a spell, and then it "consumes" the effect. Casting further spells will not trigger the effect again unless the Spellburst effect is refreshed somehow (i.e returning the Spellburst minion to your hand and playing it again).
Keywords that Work Great with Spellburst
As the effect is triggered based on your spell casting, spell related keywords, such as Spell Damage or Twinspell go with Spellburst quite well. Diligent Notetaker for instance, can copy a damaging spell while you have Spell Damage, adding the spell back to your hand, and allowing you to cast that spell with Spell Damage again.
Playing Against Spellburst in Hearthstone
The important thing to remember is that Spellburst is a one-time effect. After the Spellburst effect is used, that part of the text is essentially removed from the card, so if you're decided whether to not to kill the Spellburst minion at that point, you can picture the card as if it didn't have that text.
If your opponent summons a Spellburst minion, but didn't trigger its Spellburst effect on the same turn that they summoned it, you may want to destroy that minion before your opponent's next turn where they will have a chance to use the Spellburst effect.
Example Hearthstone Spellburst Cards
Diligent Notetaker's Spellburst effect will add a copy of the spell used to trigger the effect to your hand, which can be used to copy a myriad of useful spell effects.
Goody Two-Shields is a minion with Divine Shield, that gains another Divine Shield when Spellburst is used. Ideally, you'll want to consume the initial Divine Shield first, then cast a spell to give it the Divine Shield from Spellburst. As this will most likely require a turn to set-up, your opponent will have a chance to remove it before you can optimally use this effect. You may also wish to take care and avoid casting a spell whilst it already has Divine Shield as this will consume the Spellburst effect and waste it.
Headmaster Kel'Thuzad is a Legendary minion which uses the keyword, and is an example of how some Spellburst effects may require the spell to perform a specific task or scale based on various parameters. In this case, the Spellburst effect will summon a fresh copy of all minions that were destroyed by the spell used to trigger the Spellburst. Do be careful as the first spell you cast after you play him will consume the Spellburst trigger even if doesn't destroy any minions, meaning you will need to consider your card order when you play him.