Royal Magical Library
Effect Monster (Spellcaster / LIGHT / 4 Stars / ATK 0 / DEF 2000)
Each time you or your opponent activates 1 Spell Card, put 1 Spell Counter on this card (max. 3). By removing 3 Spell Counters from this card, draw 1 card from your Deck.
It is an Effect Monster Card. It doesn't require any Tributes in order to Normal Summon or Set it.
This card is fairly straightforward. This card has two effects: the first sentence is one, and the second sentence is the other. Let's analyse them.
Each time you or your opponent activates 1 Spell Card, put 1 Spell Counter on this card (max. 3).
This is the first effect. It is a Continuous effect, meaning it does not use a chain, and you cannot activate a card in response to it. Whenever someone activates a Spell Card, Royal Magical Library will gain 1 Spell Counter, and it can have a maximum of 3 Spell Counters on it at any one time.
A Spell Counter is a kind of marker, and can be denoted by paper-clips, pebbles, coins, a tally on a piece of paper, anything. As long as you have a way to keep track of how many Spell Counters your card has, it's fine. There are some cards that use and affect Spell Counters, and Royal Magical Library is one of them.
By removing 3 Spell Counters from this card, draw 1 card from your Deck.
This is the second effect. It is an Ignition effect, and can only be activated in your Main Phase 1 or Main Phase 2. It is a Spell Speed 1 effect, meaning it cannot be chained to the activation of another card. Trap Cards and Quick-Play Spell Cards can be chained to this effect.
You can only activate this effect when Royal Magical Library has 3 Spell Counters. By removing those 3 Spell Counters, you get to draw 1 card from your Deck.
I'd guess you've bought the Yugi Advanced Starter Deck, am I right?