Here is an excerpt from Max Lucado on how to let go of anxiety. Warning: it’s a tad simplistic. It doesn’t address the biological component of anxiety at all and therefore is somewhat unauthentic. But I do like his reminder of going to God with our worry. For the full excerpt, click here.

The burlap bag of worry. Cumbersome. Chunky. Unattractive. Scratchy. Hard to get a handle on. Irritating to carry and impossible to give away. No one wants your worries.
The truth be told, you don’t want them either. No one has to remind you of the high cost of anxiety. (But I will anyway.) Worry divides the mind. The biblical word for worry (merimnao) is a compound of two Greek words, merizo (“to divide”) and nous (“the mind”). Anxiety splits our energy between today’s priorities and tomorrow’s problems. Part of our mind is on the now; the rest is on the not yet. The result is half-minded living.
That’s not the only result. Worrying is not a disease, but it causes diseases. It has been connected to high blood pressure, heart trouble, blindness, migraine headaches, thyroid malfunctions, and a host of stomach disorders.

Anxiety is an expensive habit. Of course, it might be worth the cost if it worked. But it doesn’t. Our frets are futile. Jesus said, “You cannot add any time to your life by worrying about it” (Matthew 6:27). Worry has never brightened a day, solved a problem, or cured a disease.
How can a person deal with anxiety? You might try what one fellow did. He worried so much that he decided to hire someone to do his worrying for him. He found a man who agreed to be his hired worrier for a salary of $200,000 per year. After the man accepted the job, his first question to his boss was, “Where are you going to get $200,000 per year?” To which the man responded, “That’s your worry.”
Sadly, worrying is one job you can’t farm out, but you can overcome it. There is no better place to begin than in verse two of [Psalm 23,] the shepherd’s psalm.
“He leads me beside the still waters,” David declares. And, in case we missed the point, he repeats the phrase in the next verse: “He leads me in the paths of righteousness.”
“He leads me.” God isn’t behind me, yelling, “Go!” He is ahead of me, bidding, “Come!” He is in front, clearing the path, cutting the brush, showing the way. Just before the curve, he says “Turn here.” Prior to the rise, he motions, “Step up here.” Standing next to rocks, he warns, “Watch your step here.”

He leads us. He tells us what we need to know when we need to know it. As a New Testament writer would affirm: “We will find grace to help us when we need it” (Heb. 4:16 NLT, emphasis mine).
Listen to a different translation: “Let us therefore boldly approach the throne of our gracious God, where we may receive mercy and in his grace find timely help” (NEB, emphasis mine).
God’s help is timely. He helps us in the same way a father gives plane tickets to his family. When I travel with my kids, I carry all our tickets in my satchel. When the moment comes to board the plane, I stand between the attendant and the child. As each daughter passes, I place a ticket in her hand. She in turn gives the ticket to the attendant. Each one receives the ticket in the nick of time.
What I do for my daughters God does for you. He places himself between you and the need. And at the right time. He gives you the ticket. Wasn’t that the promise he gave his disciples? “When you are arrested and judged, don’t worry ahead of time about what you should say. Say whatever is given to you to say at that time, because it will not really be you speaking; it will be the Holy Spirit” (Mark 13:11, emphasis mine).