Like any other language, you will need to formally learn the basics of Mandarin/ Putonghua, so best enroll in a course to understand and learn basic grammar, tones etc. Shenzhen speak mainly Putonghua, but also Cantonese and a small amount of English. Maybe it is better if you move to a larger city like Shanghai or Xian, Beijing ( where locals claim that they speak perfect English, or Chinglish but know nothing about Western customs/ behaviour.)
I used to travel up to Shenzhen often, and the Putonghua is quite rough compared to larger cities with more western influence. Maybe that could be your starting point. I was in Harbin this time last year, and the Mandarin/ Putonghua is unbelievably rough compared with large cities with some western influence. Only speaking from personal experience . Good luck, and stay positive, like learning any new lingo, you will make mistakes. But keep a sense of humour among those who don't.