The short answer to the question of how to translate “technology” or “technique” into German is the word Technik. It refers to all measures, processes, and applications that make knowledge gained from the natural sciences useful for humanity as well as to a particular or specially defined method of doing something (i.e. “technique”). It also refers to technical equipment.
The German word Technologie, on the other hand, refers to the science of transforming raw materials into finished products using scientific methods, and for this reason is usually used as a component in larger words (e.g. Biotechnologie, Nanotechnologie, etc.). Technologie also encompasses all processes involved with acquiring and processing materials.
However, due to the influence of English, nowadays, both terms are often used synonymously in spoken German (except in the sense of “technique”, which is always Technik).
Wir benutzen die modernste Technik. We use the most modern technology.
Sie hat eine besondere Technik erlernt. She’s acquired a special technique.