Many consider the last words of Jesus to be the most important words.
And He said to them, "Go into all the world and preach the gospel to every creature. He who believes and is baptized will be saved; but he who does not believe will be condemned. And these signs will follow those who believe: In My name they will speak with new tongues; they will take up serpents; and if they drink anything deadly, it will by no means hurt them; they will lay hands on the sick, and they will recover." And they went out and preached everywhere, the Lord working with them and confirming the word through the accompanying signs. Amen
When we read the last part it sounds like the Lord is working with "them" - the disciples - and confirming the word. However, the word "they" does not exist in the original text, but was added by the translators in an effort to make the text more fluent. Leaving that word out is perfectly appropriate since it is not there in the original text. If we read it without the word "they" we gain a better understanding of what Jesus is saying:
"And they went out and preached everywhere,
the Lord working with and confirming the WORD through the accompanying signs."
The Lord works with the WORD and confirms the WORD with signs following. Thus, it reiterates how important the WORD is when we try to win people for God. The disciples themselves were not extra special people who were able to do special miracles and healings. All believers are able to be effective, because it's not about us, but about the power of the WORD. The Holy Spirit works with the WORD that we speak and will confirm it with signs following. Paul wrote that it is the Gospel that is "the power of God to salvation for everyone who believes". (Romans 1:16)
We can extrapolate 4 crucial points from Mark 16:15 (quoted above) and apply it when we have family members or friends who are lost:
(1) Take authority over the devil - "In My name they will cast out demons"
Jesus is instructing His disciples to go out into all the world and spread the Gospel, the WORD and as they spread the WORD, these signs will follow them. The first sign is that they will cast out devils. This means that as a believer you must put the Name of Jesus in your lips, you must have faith in the Name of Jesus, and you have to believe that when you speak the Name of Jesus, demons are afraid and they will flee.
When you're praying for a rebellious child, wayward son, or unsaved spouse you must start here. Take authority over your family member. Jesus gave us authority in His Name and we do not battle against flesh and blood (Ephesians 6:12)
This does not mean you must walk up to the person and speak these words over them. Go into your prayer closet and speak these words, for example: "Satan, in the Name of Jesus, you have no right to touch my family. I place a hedge of protection around this person. I bind all demonic powers, principalities and rulers of darkness who are affecting this person."
Jesus said, "whatsoever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven." (Matthew 18:18)
We must remember that the God of this world is Satan (2 Corinthians 4:4), therefore all illness, disease, natural disaster or calamity is from Satan, not of God. God IS sovereign and all-powerful, however He has allowed Satan control over this world for a period of time and then there WILL BE an accounting - a Day of Judgment. In the meantime, we are battling the god of this world and his wicked spiritual beings. But God has given us the tools and armor to fight this war - Ephesians 6.
(2) Pray in the Spirit - "They will speak with new tongues"
Remember when you pray, not to ask for things that God has told YOU to do. Do you ask God to remove the hornet that flew into your house, or do you take up a broom and shoo the thing out yourself?
Paul said that "he who speaks in a tongue does not speak to men but to God, for no one understands him; however, in the spirit he speaks mysteries." (1 Corinthians 14:2) The human heart is a mystery and we cannot always know what the exact reason is a person will not accept Jesus. We cannot know what is hindering that person from hearing and accepting the Word - the Good News of salvation. Praying in our own language covers the known stuff, but praying in the spirit covers the unknown stuff - the things that are mysteries to us.
The most effective prayer is the one that is in the spirit, because it removes the pride of the petitioner, as well as their preconceived notions and judgments.
Therefore, pray once in your own language and pray in the spirit from that point forward. God is not deaf that you need to repeat the same petition over and over again, begging Him to do something. As a Christian, you are not praying to a stick or stone, you are praying to the Living God, who hears your prayer. Next time your family member is on your mind, you could say, "Praise God, You've already heard my prayer and I don't have to keep on asking for it ..." and then proceed to pray in the spirit so that the "Spirit Himself makes intercession for us with groanings which cannot be uttered. Now He who searches the hearts knows what the mind of the Spirit is, because He makes intercession for the saints according to the will of God." (Romans 8:26-27) Every time you pray in the spirit you can be assured that you are praying the will of God.
If you've been praying over and over and over again for the salvation of a person and it's not happening, your prayer is ineffective. It should tell you that you're missing something. Have you considered praying in the spirit and allowing the Spirit to intercede on your behalf?
(3) Be Bold - " the will take up serpents, and if they drink anything deadly it will by no means hurt them."
Paul encountered a deadly viper when he was shipwrecked on Malta. The natives first thought he must be a murderer and that justice has been done by the viper, but when he just "shook off the creature into the fire and suffered no harm", "they changed their minds and said that he was a god." (Acts 28:1-6)
Be bold and not fearful. Boldness is an essential key to receiving from God. It does not mean that you should be brass, or loud, or arrogant. It also does not mean you should go out and pick up snakes, drink poison and do other daring things. It does mean that we should not be fearful or hesitant to speak when we have an opportunity to speak. When we do speak, however, let it be in a loving, kind and positive manner. The Good News of the Gospel is "GOOD NEWS", and we should be able to convey that positive and wonderful message to others.
Paul, the most bold of all the apostles, prayed many times for boldness. (Ephesians 3:12, Acts 4:29)
(4) Heal - "They will lay hands on the sick, and they will recover."
Use every opportunity to show the healing power of God by laying hands on the sick. Why do we have power over sickness? Because the Gospel says that Jesus is the only One who was born sinless, He died for sin and He took away sin along with the consequences of sin, which is sickness, poverty and eternal death.
God may answer your prayer and bring about your sincere petition for the salvation of another person in numerous ways. He might just give you the opportunity to heal them when they are sick. It's just a matter of time for one of your family members, or persons you are interceding for, to get sick. If you lay the ground work, steps 1-3 very well, when that opportunity comes, you will be able to act with confidence and lay hands on them.