If I move my Irresistable Faefolk to a battlefield and use its ability to pull an enemy unit to that battlefield, how...

When you move your Irresistible Faefolk to an unoccupied (uncontrolled) battlefield and use its ability to move an enemy unit to that same battlefield, you become the attacker and the enemy unit becomes the defender.

According to RiftJudge FAQ #9828, #9665, and #9714, the designation of attacker and defender is determined by which player applies the "Contested" status to the battlefield first (Rule 459.2.b.1). Because you initiated the move that contested the empty battlefield, you are the attacker, and the enemy unit moved by your ability joins the combat as the defender.

Sequence of Events

1. Move: You move Irresistible Faefolk to an unoccupied battlefield. This applies the "Contested" status to that battlefield. Because you are the player who applied this status, you gain the Attacker designation.
2. Trigger: Irresistible Faefolk's ability ("When I move to a battlefield...") triggers. You place this ability on the chain.
3. Resolution: When the ability resolves, you choose an enemy unit and move it to that same battlefield.
4. Combat Transition: Because units from opposing players are now present at the contested battlefield, the showdown transitions into a Combat Showdown.

Even though your ability moved the enemy unit, you remain the attacker because you were the one who initiated the combat by applying the "Contested" status to the battlefield first.