So if I activate an ability of a Chandra planeswalker and use the first ability of the Chandra's Regulator can I activate it multiple times? Or am I limited to just one copy?
It is not an activated ability, so you don't "activate" it. Yes, it has a cost, but it's not in the (cost): (effect) format all activated abilities follow.
It is a triggered ability. It triggers only once each time you activate an loyalty ability from Chandra. When this trigger resolves, you can either pay 1 or not; if you do, it copies Chandra's ability. It's not "pay X, copy it X times" or "for each time you pay 1", so you can only pay 1 per Regulator per Chandra ability.
So if I activate an ability of a Chandra planeswalker and use the first ability of the Chandra's Regulator can I activate it multiple times? Or am I limited to just one copy?
Like so many beginners, you're probably confusing ACTIVATED abilities with TRIGGERED abilities.
A triggered ability is not under your direct control: it happens 'by itself' when the gamestate matches its trigger condition, and all you can do is deal with it. Regulator's ability says "you may pay 1", and that's all you can do: pay 1, or don't pay, your choice.
Some triggered abilities do allow for a variable action. Vigil for the Lost, for example, allows a choice on the amount you'll pay.
An activated ability, on the other hand, is something you have full control over: you decide if and when you want to use it. The other ability of Chandra's Regulator, for example, is an activated ability: you choose if and when you want to discard a card to draw another.
602. Activating Activated Abilities
602.1. Activated abilities have a cost and an effect. They are written as “[Cost]: [Effect.] (…)”
603. Handling Triggered Abilities
603.1. Triggered abilities have a trigger condition and an effect. They are written as “[When/Whenever/At] [trigger condition or event], [effect]. (…)”
603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. (…)
It is a triggered ability. It triggers only once each time you activate an loyalty ability from Chandra. When this trigger resolves, you can either pay 1 or not; if you do, it copies Chandra's ability. It's not "pay X, copy it X times" or "for each time you pay 1", so you can only pay 1 per Regulator per Chandra ability.
A triggered ability is not under your direct control: it happens 'by itself' when the gamestate matches its trigger condition, and all you can do is deal with it. Regulator's ability says "you may pay 1", and that's all you can do: pay 1, or don't pay, your choice.
Some triggered abilities do allow for a variable action. Vigil for the Lost, for example, allows a choice on the amount you'll pay.
An activated ability, on the other hand, is something you have full control over: you decide if and when you want to use it. The other ability of Chandra's Regulator, for example, is an activated ability: you choose if and when you want to discard a card to draw another.
602.1. Activated abilities have a cost and an effect. They are written as “[Cost]: [Effect.] (…)”
603. Handling Triggered Abilities
603.1. Triggered abilities have a trigger condition and an effect. They are written as “[When/Whenever/At] [trigger condition or event], [effect]. (…)”
603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. (…)
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules