I'm a British citizen married to a non EU, and I want to move to live and work in Germany, my question is what is the easiest why to bring my wife with me to Germany and how can I apply for a residence permit card for my wife Thanks
You should apply for a "Residence card for family members of EU (except Germany) and EEA citizens." See, for example, https://service.berlin.de/dienstleistung/324282/en/.
If your spouse is a "visa national," requiring a visa to enter the Schengen area, you will need to apply for a visa before entering Germany. Under the relevant EU directive, this visa must be issued free of charge, but a cursory search of the web site of the German Consulate in New York did not locate the correct page with the details. The EU rules are explained here: http://europa.eu/youreurope/citizens/travel/entry-exit/non-eu-family/index_en.htm