Depends on if you are asking whether you can converse with God or if you are asking if God still converses with the whole human race or a group of people like Moses with Israel. If it's with you, God answers prayers when they are from the heart. Sometimes the answer is no. How he responds would be two methods. The light of Christ which is in all things that gives us our conscience to choose good over evil. Or, the influence of the Holy Ghost which is a member of the Godhead.
When it comes to God speaking to mankind, it only can come one way, through a prophet. Apostles are also prophet, seers and revelators. Amos 3:7, "Surely the Lord God will do nothing, but he revealeth his secret unto his servants the prophets."