1.添加Newtonsoft.Json引用(我用的VS2015 ASP.NET应用程序默认有此引用);
2.引入命名空间;
using Newtonsoft.Json;
3.转换为JSON字符串格式;

public string Get(int id)
        {
            try
            {
                SqlConnection sqlConnection =
                    new SqlConnection(
                        "Data Source=127.0.0.1;Initial Catalog=GaryWeb;Integrated Security=True;User Id=sa;Password=123456");
                sqlConnection.Open();
                string sql = "select * from Users";
                DataSet dataSet = new DataSet();
                SqlDataAdapter sqlDataAdapter = new SqlDataAdapter(sql, sqlConnection);
                sqlDataAdapter.Fill(dataSet);
                return JsonConvert.SerializeObject(dataSet);
            }
            catch (Exception ex)
            {
                return ex.ToString();
            }
        }

关键代码:JsonConvert.SerializeObject(dataSet);