How can I validate DataGridView input?

I believe you are looking for DataGridView.DataError event. you should handle this event if you want to have custom validation on data. something like this:

    private void Form1_Load(object sender, EventArgs e)
    {
        dataGridView1.DataSource = entities;
        dataGridView1.DataError += new DataGridViewDataErrorEventHandler(dataGridView1_DataError);
    }

    void dataGridView1_DataError(object sender, DataGridViewDataErrorEventArgs e)
    {
        // you can obtain current editing value like this:
        string value = null;
        var ctl = dataGridView1.EditingControl as DataGridViewTextBoxEditingControl;

        if (ctl != null)
            value = ctl.Text;

        // you can obtain the current commited value
        object current = dataGridView1.Rows[e.RowIndex].Cells[e.ColumnIndex].Value;
        string message;
        switch (e.ColumnIndex)
        {
            case 0:
                // bound to integer field
                message = "the value should be a number";
                break;
            case 1:
                // bound to date time field
                message = "the value should be in date time format yyyy/MM/dd hh:mm:ss";
                break;
            // other columns
            default:
                message = "Invalid data";
                break;
        }

        MessageBox.Show(message);
    }

you can check the value of entered data and show appropriate error message for that value. for example if value is null or empty and the field is not nullable, you can show a message indicating that the value cannot be empty.

Hope this helps.