The answer for this is really three pronged and is true for whatever you fill in the X with. The question was asked about Jehovah's Witnesses, but it could just has easily been Mormon, Islam, Buddhist, or atheist, or agnostic.
The first thing to do is to seek the baptism in the Holy Spirit yourself. You need the Holy Spirit's help when you are witnessing to anyone, both for when, how, where, and what to say. There is really no substitute.
It doesn't hurt to find out a little about how their beliefs differ from Christianity if they think of themselves as Christian or followers of God which would encompass the first two listed. If you know where the differences are at you will be prepared to show where the Bible tells what is really true. But you also need to be prepared in that most of these groups will have just as many points they will make in trying to move away from the Bible or the New Testament to their books that form the basis of their belief system. That is why the Holy Spirit is so important and why it is important that you know the Bible yourself so the Holy Spirit will have resources to draw on.
But the most important thing that you can do is point out what God has done for you and for people who are alive today that you personally know. Satan cannot battle contemporary truth that you are speaking. He can make people doubt it or try to ignore it just like he makes people try to believe that the Bible isn't true. Contemporary truth is something that is hard to fight.
An elderly man in my Sunday School class relates that when he was a child he would routinely ride out on his bike in the morning and not be expected home till it was dark. One evening got a flat tire as he was hurrying home as darkness approached and was worried that he would be late if he had to push his bike home and would get in trouble. He prayed and when he looked down his tire was inflated and whole again so he could peddle home. That's a miracle of today. The people who read about this account may scoff, but the man holds it as fact.
An elderly woman with a history of heart problems was having heart pains one night, but decided she had lived a long life and was ready to go home if that was what God wanted, so she didn't go to the emergency room. When she got up the next morning she felt fine and when she turned to her daily Bible reading in the Psalms it was one speaking of God's healing. To this day (and it's been many years) she has had no more heart problems. I've had other healings occur in my family as well.
Another lady was having trouble with coughing and went to the doctor and got an X-ray. The doctor said it looked like cancer and he would need to biopsy it to be sure and scheduled it for Monday. That Sunday she had people pray for her and her coughing stopped and she felt better. When she went in to see the doctor the next day she told him and asked him to take another X-ray to check before doing the biopsy, and the X-ray was clear.
Our pastor suffered allergies as a child that were horrible and even if treatment was available, they couldn't afford it. He just had to suffer through day in and day out. His mom went with a neighbor to a mid-week church meeting. While they were gone, the pastor felt prompted to look at the time so he did. When his mom came home she asked how he was and he said that other than a couple of times blowing his nose, he was doing much better. She asked when it happened and he remembered the time. It was when the group where she was was lifting him up in prayer. He hasn't had any issues with allergies since.
The pastor related some history of Douglas Clay. His father, a pastor, died when he was young and at the funeral where the district superintendent officiated, he wrote a message that he would take care of his mom and carry on his father's work on the back of a tithing envelope and when he passed the casket he put the envelope in the pocket of his father's suit. Years passed and he went on to bible college, but was really struggling with whether he was on the right course in seeking to be a minister. He was in the choir at the college and after practice a girl came up to him and gave him a note and said her mom had told her to give it to him when she saw him. It was the tithing envelope. The girl was the daughter of the superintendent who had officiated at his father's funeral. Her mother had seen him put the envelope in his father's suit and had felt led by the Holy Spirit to take it and keep it all those years. Then when the time was right the Holy Spirit had prompted her to give it back to the young man at the time when Satan was working hardest to sew doubt about his future. The young man has gone on in life to be the head of the Assemblies of God.
Never doubt that God has a plan for your life or that He doesn't care about you. God is still at work today, just like He was in the New Testament times. He hasn't changed. He's still speaking with his people. Will we hear His call on our heart?
Be filled with the Spirit. Let Him be your guide as to how to interact with your friend. He'll tell you when the right time is to speak and what to say if you are close to Him. In the mean time, study Christianity. Study the Bible. Learn. Make yourself ready. And don't forget all the things God is doing for you and has done for you. Let other Christians know. It will be good practice for telling the basis of your faith to your friend. Try to remember some of the things that God has done for others in your community and state. It is great that God is working in other countries, but if it is someone you can directly put your friend in contact with if they doubt it is better.
Then it will be up to them to weigh what your faith has done for you. Ultimately, it is their choice to make. You cannot make it for them. All you can do is let the fruit of the Spirit and gifts of the Spirit of God work in your life and be a witness. Sometimes your very life will be the most important and powerful witness you will ever have.