How to travel from hongkong to shenzen and how to travel in less cost.? And things to do in SZ?

You can take the East Rail Line to reach Lo Wu, and then pass the port to reach SZ. There you can take the local subway to any place you want to go.
In that city, Window of the World, Happy Valley, Splendid China, Dameisha & Xiaomeisha Scenic Area, Meridian View Center, Minsk World, Overseas Chinese Town East, Shenzhen Safari Park, Xiaomeisha Sea World and Xili Lake Resort are all good places to visit.