Nikita, I love this question! I personally do believe that God does speak to us today in many ways. The God of the Bible is a God who loves us, who sees us, who hears us and who cares for us. He is a God who wants a relationship and a relationship always involved communication.
If you had a friend who always does all the talking (husbands maybe you are thinking of your wives right now?!) but you never had the chance to respond then what kind of relationship is that. Followers of Jesus communicate with God through prayer, but prayer is not just us talking to God or at Him.
Prayer should be a two way line of communication. I believe today that three main ways God speaks to people are through His word (the Bible), through prayer, and through the local church. If God is speaking to you and you are unsure if it is from God or not one sure way to check is to align it with the Word of God. God will never tell you to do something that goes against what the Bible says to be true.
This is why it is important to always go back to God’s Word when we believe God is speaking to us. In addition to that God will speak to us through our times of prayer. As we speak to God in prayer and take time to listen the Spirit of God will also speak to our hearts during our times of prayer.
Finally, I believe that God also speaks to us through the local church. As followers of Jesus we were not called to walk this journey alone, but rather in gospel community. God has given us the local church to worship him and grow in our relationship with God as the family of God. God will use other believers in our life to point out sin in our life, encourage us, and help guide us.
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