This passage can be understood two ways. One way is to assume that Jesus followers are expected to handle deadly snakes to prove to unbelievers that they are Christians. Another way to understand this passage is to be reassured that when Christians accidentally come in contact with poisonous snakes, God will miraculously protect them.
In looking at the subsequent history of the New Testament Church, the Bible records only the latter explanation—that if a true Christian accidentally picks up a poisonous snake and is even bitten by that snake, God can intervene to miraculously spare that persons life.
Such an experience happened to the apostle Paul. After being shipwrecked and escaping to the island of Malta, Paul was bitten by a deadly snake. The natives thought he would die, but God miraculously intervened and Paul was not harmed (Acts 28:1-6).
Additionally, the Bible tells us that we should not tempt God by deliberately placing ourselves in potential danger (Matthew 4:5, 7). Based on these scriptures, we can conclude that God does not want us to handle poisonous snakes today to prove we are Christians. We can also be assured that God continues to perform miracles in healing and protecting those who trust and believe in Him.