Spells cast from the ring use normal actions and no components.
Many magic items allow the user to cast spells. The general rules for this are on p. 141 of the DMG, under the Spells subsection of Activating an Item:
Some magic items allow the user to cast a spell from the item. The spell is cast at the lowest possible spell level, doesn't expend any of the user's spell slots, and requires no components, unless the item's description says otherwise. The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration.
Beyond these rules for magic items, casting a spell follows the rules in the Player's Handbook; generally, the character casting the spell takes the Cast a Spell action on their turn.
Here's what the Ring of Spell Storing says about casting the spells in it (DMG, p. 192:
While wearing this ring, you can cast any spell stored in it. The spell uses the slot level, spell save DC, spell attack bonus, and spellcasting ability of the original caster, but is otherwise treated as if you cast the spell.
Let's look at two examples of stored spells being cast:
- Fireball stored in the ring at 3rd level by a 10th Level School of Evocation wizard with a save DC of 16
- Magic Circle stored in the ring at 5th level by a 11th level Cleric with a save DC of 17.
Fireball, cast from the ring by a 3rd level Sorcerer (save DC 14):
- Will require one action to cast (same as the spell)
- Will do 8D6 damage; the original casting wizard's Empowered Evocation feature will not apply since it is not one of the characteristics that the ring lists as being 'stored'.
- Can be used with Quickened Spell by the casting sorcerer, since that falls under being "treated as if you cast the spell".
- Will have a save DC of 16, from the original caster.
Magic Circle, cast from the ring by a 19th level Fighter:
- Will require one minute to cast (same as the spell).
- Will not require any chalk or other material components, even though that is normally required.
- Will have a duration of three hours (base duration plus two extra hours for using a 5th level slot).
- The fighter has no spellcasting ability, and thus no spell save DC, but the Magic Circle will have a save DC of 17.
Based on the wording there, I would be inclined to say that it cannot wild surge when cast from storage unless the wild mage is also the one casting it from storage.
The spell uses the slot level, spell save DC, spell attack bonus, and spellcasting ability of the original caster, but is otherwise treated as if you cast the spell
This doesn't mention wild magic as one of the things that's retained from the original caster, so if someone other than the wild mage used the spell there would be no surge. If the wild mage is the one to use the stored spell, since it is treated as them casting the spell for everything not explicitly listed, I'd say there's a chance for a surge.
As for storing the spell, it says that the spell has no effect, but the description of the Wild Magic Surge feature says
Immediately after you cast a sorcerer spell of 1st level or higher, the DM can have you roll a d20. If you roll a
1, roll on the Wild Magic Surge table to create a random magical effect.
This strongly suggests that the wild magic effect is not part of the spell itself, as it happens after your cast the spell. In particular, no wild surge effect modifies the spell that triggered it. So it seems fair to say that storing the spell can trigger a surge.
No, someone already spent a spell slot (or slots) by filling up the slot(s) in the ring
I italicized "cast into it" and "as the spell is cast" as a link to basic rules on spell casting.
As an example: a Fighter (Champion) can cast a stored spell from this ring without even having spell slots from their class (they have no spell slots), once they are attuned to the ring that has spells already stored in it.
For what it's worth, we have a lot of related questions on the Ring of Spell storing. You may find them all of interest, since it's a very versatile item. My first D&D group applied this approach to provide familiars for multiple characters by using the ring.
To answer your comment:
Yes, that is a way to use it (preparation). Think of it as a wallet. You put some cash into it and you can go and spend the cash while shopping. Then it's empty. You have to put some more cash into it to fill it up before the next shopping trip.