First you need to use DateTime.Parse()
to create a .NET DateTime object from the string value, as noted by others.
Don't be tempted to do something like:
var sql = "INSERT INTO MyTable VALUES(" + someDate.ToString() + ")";
It's much better to build a parameterized query instead, not just in this case. It also makes sure that if you're trying to insert/update text, you're able to handle quotes correctly (instead of risking a sql injection possibility)
using (var conn = new MySqlConnection(connectString))
using (var cmd = new MySqlCommand("INSERT INTO mytable VALUES (1, 2, @theDate)", conn))
{
cmd.Parameters.AddWithValue("@theDate", someDate);
cmd.ExecuteNonQuery();
}