Add your button.
Add a Click handler to your button.
Then in the click handler, read the text from the TextBox.
Then all you have to do is an SQL INSERT to add it to your DB.
Exactly how you INSERT will depend on what DB system you are using, but this will save a string and a DateTime value to SQL Server:
using (SqlConnection con = new SqlConnection(strConnect))
{
con.Open();
using (SqlCommand cmd = new SqlCommand("INSERT INTO myTable (myColumn1Name, myColumn2Name) VALUES (@STR, @DT)", con))
{
cmd.Parameters.AddWithValue("@STR", strReadFromTextBox);
cmd.Parameters.AddWithValue("@DT", DateTime.Now);
cmd.ExecuteNonQuery();
}
}