use cell click event
in the event just assign cell.backcolor to color.red
private void GridView_CellClick(object sender, DataGridViewCellEventArgs e)
    private void GridView_CellClick(object sender, DataGridViewCellEventArgs e){
        DataGridViewCellStyle CellStyle = new DataGridViewCellStyle();
        CellStyle.BackColor = Color.Red;
        dataGridView1.Rows[e.RowIndex].Cells[e.ColumnIndex].Style = CellStyle;
    }
You can change the DefaultCellStyle. For example:
...
dataGridView1.DefaultCellStyle.SelectionBackColor = Color.Red;
...
DataGridViewCell cell;
cell = datagridview1[0,0];  // location of cell
cell.Style.BackColor = Color.LimeGreen;  // or whatever color you want
This could be placed in a loop etc., using the indices.
I would recommend setting it in the Cell_Enter event
OR
void dataGridView1_CellFormatting(object sender, DataGridViewCellFormattingEventArgs e)
{
     if (e.Value != null)
     {
         if (condition)
            e.CellStyle.BackColor = Color.FromArgb(255, 160, 160);
     }               
}
Update from 2022, working with Visual Studio 2022, to the right answer of the user @Umesh CHILAKA.
DataGridViewCellStyle has BackColor property, meaning you can access this directly, so you can consider to use the following, as it will work too:
dataGridView1.Rows[e.RowIndex].Cells[e.ColumnIndex].Style.BackColor = Color.Red
Another plus of this aproach is that you don't create another object DataGridViewCellStyle.
 
         
                                         
                                         
                                         
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