There is so much we could say here. I think the following four points will give you a lot to work on.
Start by building up your faith
Since true importune prayer is aroused and energized by the Holy Spirit, it makes sense that if you want to pray with importunity you must be filled with the Spirit and walk in the Spirit. You can begin to do this by meditating on the Word. When you get to know the God of the Word you will learn to trust Him and wait on Him in prayer. Soon you will not yield to discouragement and weariness when you pray. Likewise, you will say to God, “O my God, I trust in You” (Ps. 25:2). And you will keep praying persistently for as long as it takes to gain the answer.
Strengthen your friendships
Since friendship is a great motivating factor in importune prayer, it behooves us to strengthen our friendships. Strengthen your friendship with God by spending more quality time in the Word and by spending more intimate time with Him in prayer. Likewise, you can strengthen your human friendships basically the same way, by spending more time with them. In your time together of course, you ought to seek to get to know each other by asking personal questions and by praying together. But the most important thing I think is to play together. Yes, have fun together (as children do); and, with all your heart, seek to enjoy yourself with that person. Out of your mutual enjoyment of each other will come a deep concern and love for each other. This deep friendship will energize your persistent prayers for each other like nothing else.
Stretch out your praying
Plan your prayer times, and plan to pray for as long as possible. When you can, pray for an extended period of time: for a couple of hours, a half a day, or even a whole day. Don’t let petty activities get in the way of your praying. Set your priorities on prayer. When you are in the habit of praying longer, God will bless you and give you great joy. He will make you want to spend more and more time in prayer. You will never want to quit until He tells you, Stop praying now until our next meeting. I like what E. M. Bounds has said: “Importunate prayer has patience to wait and strength to continue. It never prepares itself to quit praying, and declines to rise from its knees until an answer is received.”6
Don’t give into laziness and selfishness
Importune praying requires a lot of work and is never selfish. If you want to pray with importunity, guard against the love of ease and seeking always to please yourself. Instead practice thinking and praying for the needs of others. Try to feel and experience their hurts and needs as your own. Put yourself in their place. Ask yourself, “How would I feel and what would I do if I were them?” This practice will put you right on the cutting edge of prayer. It will give you the passion and patience to continue in prayer for a person for as long as it takes.
6 E. M. Bounds, The Necessity of Prayer, p. 73.