What does the Holy Spirit do?

The Bible likens the Holy Spirit to fire (Isaiah 4:4), wind (John 3), water (7:37–39), a dove (Genesis 1:2; Luke 3:22), a "seal for the day of redemption" (Ephesians 4:30; 2 Timothy 2:19), an "earnest" or down-payment on the future (Ephesians 1:13,14), and anointing oil (2 Corinthians 1:21).

But it may be easier to understand what the Spirit does by looking at what he did.

Did the Holy Spirit act in the Old Testament?

The Spirit was extremely active in the Old Testament. 

He created the material universe and humanity (Psalm 33:6; Job 33:4). He empowered individuals for specific tasks (Judges 14:6,19; 15:14; 1 Samuel 10:6,10; 2 Chronicles 15:1–2; Zechariah 4:6). He maintains living creatures (Psalm 104:29, 30), and sides with the helpless, poor, wretched and oppressed (103:6).

He anticipated the Anointed One, the Messiah (Isaiah 42:2), and would one day be poured out on the house of Israel (Ezekiel 39:29). He would be experienced universally (Joel 2:28–29) and would write God's laws on the hearts of all (Jeremiah 31:31–34).

What did the Holy Spirit do in the New Testament?

The Spirit was active in the life and earthly ministry of Jesus. 

Our Savior was born of the Spirit (Luke 1:35) and lived a sinless life in the power of the Spirit (Hebrews 9:14). He was anointed and fitted for service by the Spirit (Acts 10:38; Isaiah 61:1; Luke 4:14,18,19; 3:22). 

The Spirit led Jesus in his earthly movements (Luke 4:1). He taught Jesus and was his source of wisdom (Isaiah 11:2,3; 42:1, fulfilled in Matthew 12:17,18).

Jesus worked his miracles through the Spirit (Matthew 12:28). By the power of the Spirit, Jesus was raised from the dead (Romans 8:11). 

After his resurrection, Christ gave commandments to his apostles through the Spirit (Acts 1:2). Now the Spirit bears witness to Jesus (John 15:26, 27).

The Spirit then worked in the apostles and prophets, giving them special gifts for specific purposes (1 Corinthians 12:4,8–11, 28, 29). Truth was hidden before the Spirit revealed it (Ephesians 3:3–5). The apostles and prophets spoke not in their wisdom but the Spirit's (1 Peter 1:10,12) as they were carried along by him (2 Peter 1:21). 

Does the Holy Spirit still speak today?

The Spirit spoke prophetic utterances (Hebrews 3:7; 10:15, 16; Acts 28:25; 2 Samuel 13:2), so that when we read their words we find not the speech of men but of God (Mark 7:13; 2 Samuel 23:2). 

In a very real sense, every time we open the pages of Scripture, we hear the voice of the Spirit as he speaks to us today.