"Does God still speak through people? I ask this because sometimes brothers and sisters say that God could be using them to let one know something." -- Lester Luna (Nicaragua)
Here is my understanding.
God communicates with all the world through at least a dozen ways:
  • Godly advice
  • Nature (Psalm 19; 104)
  • The history of ancient Israel (Rom 15:4; 1 Cor 10:11)
  • The prophets and apostles of old (Eph 2:20; Heb 1:1)
  • Our consciences (not infallible, but still a key safety mechanism)
  • Wisdom (the distilled wisdom of all cultures has much to teach us)
  • Relationships (since a relationship with God is analogous in many ways to relationships with people, we can learn a lot by observing)
  • Dreams (indirectly — sometimes a dream shows us what we are really thinking about, so God can get our attention this way, even though there will be no direct message)
  • The person of Jesus Christ. Christ is called “The Word of God,” and in a way the Lord speaks most clearly in the Word (even more than in the Heb 4:14 word).
  • Scriptures (both testaments)
  • Suffering ("His megaphone to rouse a deaf world" [C.S. Lewis])
But you seem to be asking about special people. Here are my thoughts:
  • The church is built on the foundation of inspired prophets and apostles (Eph 2:20; Heb 1:1). They no longer exist. The foundation was laid in the 1st century.
  • Jesus has delivered the final word. Just as with the Old Testament (if they didn’t listen to Moses and the Prophets — Luke 16 — no miracle would make any difference), so with the N.T. (no miracles required, though once in a blue moon they certainly still occur).
  • The Bible is in a class of its own. No human supplement may modify it — although practical wisdom for application of biblical principles is always important.
That's the long answer.
Short answer: No, God does not speak through prophets today. No one on the planet is inspired, chosen by God to reveal his word to others.
However, we still have:
  • Teachers — who explain and apply the word
  • Elders — who guide local churches
  • Evangelists — who proclaim the gospel as they plant churches
Not to say there aren’t others who can share God’s word, but these three positions are especially important, now that the apostolic age is past.
Hope this helps, Lester.