DataTable and DataGridView

Hi. I have followed this tutorial and i am now showing data in my DataGridView:

Code:

---

void FillData()
        {
            // 1
            // Open connection
            using (SqlCeConnection c = new SqlCeConnection(
                Properties.Settings.Default.DataConnectionString))
            {
                c.Open();
                // 2
                // Create new DataAdapter
                using (SqlCeDataAdapter a = new SqlCeDataAdapter(
                    "SELECT * FROM Animals", c))
                {
                    // 3
                    // Use DataAdapter to fill DataTable
                    DataTable t = new DataTable();
                    a.Fill(t);
                    // 4
                    // Render data onto the screen
                    dataGridView1.DataSource = t;
                }
            }
        }

---

Now I want to be able to modify the data and write it back to the database. How would i do this ? Create a function called SaveData and:
- create a connection
- create a new adapter ( that writes )
- create the datatable
- write datatable to new adapter using the connection

I was wondering if that thought process is correct. I barely have any C# coding experiences alltho this does not seem so hard. Help is appreicated

Followed this tutorial: http://dotnetperls.com/datagridview-tips