The pattern you describe is very common. When you stand up, your brain sends signals to your blood vessels to clamp down to keep blood pressure high enough so blood can reach your brain (and keep you awake!) When you lie down, you and your blood vessels tend to be relaxed, and blood can reach your brain even if your blood pressure is relatively low.
Ideally, blood pressure should be measured when you are sitting in a chair, with your legs hanging down, feet resting on the floor. Your arm should be supported by the measurer or the arm of a chair at the level of your heart. To get the most accurate readings, you should be sitting quietly for a few minutes before the reading, and avoid caffeine, smoking, and exercise for at least 30 minutes beforehand. Perhaps the most important thing to remember is to try to do it in the same position all the time, so your blood pressure readings are comparable.
