For persistent worries, it is relieving to write them down on a piece of paper and give them to God, like I described in Worries for God.
At the same time, we don't want to become so focused on the problems that we forget about our purpose. It would be exhausting to keep track of how God is doing with our worries. It is far easier to trust him and realize that the worries are less important than him, so another practice is to replace the thought of the problem with the thought of God's strength and care for us.
(Trying not to think of a problem without choosing a new focus can make us think of it more. Our new focus is God. We keep coming back to God each time our mind wanders to the problem.)
This focus could involve listening to a devotional song or an instrumental piece and really hearing it. It could involve visualizing an image of Jesus, or imagining the light of Jesus protecting us and feeling it cleanse our body and mind.
All it asks of us is a mustard seed of faith. It doesn't require great faith, but a miniscule desire to be healed and to give ourselves to God.
Through this practice, we learn that Jesus heals and that our problems are ant-sized compared to our Lord, no matter how big they may appear to us at the time.
*Try not to worry if your worry returns, just keep redirecting your attention to God. Reading an encouraging bible passage and memorizing it is very valuable, too.*
*Don't aim for perfection. If you feel a little better, enjoy your feeling of gratitude and realize that small progress is progress.*