How can I populate textboxes with data from a DataGridViewRow?

You can use SelectionChanged event since you are using FullRowSelect selection mode. Than inside the handler you can access SelectedRows property and get data from it. Example:

private void dataGridView_SelectionChanged(object sender, EventArgs e) 
{
    foreach (DataGridViewRow row in dataGridView.SelectedRows) 
    {
        string value1 = row.Cells[0].Value.ToString();
        string value2 = row.Cells[1].Value.ToString();
        //...
    }
}

You can also walk through the column collection instead of typing indexes…