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https://www.dndbeyond.com/sources/basic-rules

There’s a link to the basic rules. At the most basic example, let’s say you swing your sword at a goblin. The goblin has an Armor Class, or AC, of 15, thanks to his leather armor and shield. So in order for your swing to hit, you have to get higher than 15. So you roll a d20, and it lands on 13. However, since you’re good at swinging swords and very strong, you can add those bonuses to your roll. Let’s say +3. So your roll ends up being a 16, which beats 15. So then you roll a couple dice to see how much damage you do based on the type of weapon and how good you swing swords again. For a long sword you would roll a d8 and add any relevant modifiers to your roll. Then you subtract that number from the enemy’s go. When it’s the goblin’s turn, the DM rolls against your AC to do damage to you.

Those are the basics to all of the rolling. Someone rolls a d20 and adds modifiers to determine if they are successful at something against a target number, and the other dice are mostly for damage, healing, or to choose something random on a table.

It sounds complicated as a comment but when you play you have your character sheet which shows what all the numbers are supposed to be.

Edit: for your given example, there isn’t an ice shield spell, but there is a spell called Armor of Agathys that covers your character in frost. It gives you 5 temporary hp, and if a creature hits you in melee range (they roll higher than your AC) they take 5 damage.

Each spell has a specific description of its effects. You can cast spells at different levels depending on how strong they are, and it costs spell slots (resource points) to cast them.

So the d&d rules are fairly vast and can't be summed up all here but, the tl;dr of it:

Every attacking spell or attacking action has an associated mechanism for whether it hits or deals it's damage. Loosely, it's always one of these 3:

• You roll (a) dice, you need to beat bad guy's static number to hit them

• You have a static number, bad guy needs to roll (a) dice and beat your static number to avoid or reduce the damage

• You hit unless they specifically have an ability that makes this not the case

So, for example, "I make a melee attack with my sword against the bad guy" The bad guy has a static number of 17, I roll a (total of) 18 - it hits! Now different dice are rolled to determine damage dealt, based on the weapon.

Or

"I use magic missile on the bad guy" This spell just always hits, that's kind of its shtick. So it hits and I roll for damage, unless they counter it somehow

Or

"I use fireball on this bad guy" My static number is a total of 17, bad guy rolls a 23 - he is still hit by the fireball but will take half the damage (rounded down) when we roll for damage dealt.

Hope this helps!