Correct spelling, explanation: skier is the correct form to describe a person who skis because the base verb for this noun is ski. Here a suffix -er was used, and there is no need to double the vowel i. Because of this, the correct form is skier, not skiier.

Definition of skier:
noun, a person who skis
These professional ski boots meet the requirements of any skier.
Jack used to be a skier when he was younger, but he resigned due to an injury.

Incorrect spelling, explanation: this form is incorrect because we do not need double i when adding the suffix -er to the base word ski (ski + -er is skier). Vowels are usually not doubled with suffixes. Therefore skiier is incorrect and the correct form is skier.