A Connection Practice (a.k.a. Connection Technique) is any technique, such as meditation, mantras, relaxation, mindfulness, etc., that can a) open and enhance your connection to Consciousness/Highest Self and b) enable better control of the Flow that ensues.
The careful and guided use of Connection Supplements can facilitate connection practice.
Emanuel Swedenborg cites "hypoventilation" as a technique used to facilitate a low level Connection (Dole & Kiven, 1997).
Sharp, Michael (BOOK3). Lightning Path Workbook Three: Connection. Lightning Path Press. 
Sharp, Michael. The Great Awakening: Concepts and Techniques for Successful Spiritual Practice. Lightning Path Press.
Dole, G. F., & Kirven, R. H. (1997). A Scientist Explores Spirit: A Biography of Emanuel Swedenborg. Pennsylvania: Chrysalis books.