Q: How doth the Spirit apply to us the redemption purchased by Christ?
A: The Spirit applieth to us the redemption purchased by Christ, by working faith in us, and thereby uniting us to Christ in our effectual calling.

Ephesians 2:8. For by grace are ye saved through faith; and that not of yourselves: it is the gift of God.
John 15:5. I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.
1 Corinthians 6:17. But he that is joined unto the Lord is one spirit.
1 Corinthians 1:9. God is faithful, by whom ye were called unto the fellowship of his Son Jesus Christ our Lord.
1 Peter 5:10. But the God of all grace, who hath called us unto his eternal glory by Christ Jesus, after that ye have suffered a while, make you perfect, stablish, strengthen, settle you.

Westminster Project - See Francis Beattie on Union with Christ, Effectual Calling, and Regeneration. These are all topics covered in this section of the Catechism (Questions 29-32)