Delphi: how to make procedure on click on button array?

How about using the button's tag property to store a pointer to the correlating image. I'm unsure of your Array structure but here's a code snippet to demonstrate.

TForm1 = class(TForm)
  Button1: TButton;
  Image1: TImage;
  Button2: TButton;
  Image2: TImage;
  procedure FormCreate(Sender: TObject);

private
  FMyCurrentImage : TImage; //Keeps track of the current image
  procedure MyButtonClick(Sender: TObject);
public

end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

procedure TForm1.FormCreate(Sender: TObject);
begin
  FMyCurrentImage := nil;

  Button1.Tag := Integer(Image1);
  Button1.OnClick := MyButtonClick;
  Image1.Hide;

  Button2.Tag := Integer(Image2);
  Button2.OnClick := MyButtonClick;
  Image2.Hide;
end;

procedure TForm1.MyButtonClick(Sender: TObject);
begin
  if Sender is TButton then
    with Sender as TButton do
       if Assigned(TImage(Tag)) then
       begin
         //Hide the previously selected image
         if Assigned(FMyCurrentImage) then
           FMyCurrentImage.Hide;

         //Assign and show the clicked button's image
         FMyCurrentImage := TImage(Tag);
         FMyCurrentImage.Show;
       end;
end;

What kind of component are you using in your form to show the image?

I don't know what you really need, but here's something I guess you'd want:

I have created three components in the form to test it: two TButton's and one of TImage type.

  TfrmTest = class(TForm)
    btn1: TButton;
    btn2: TButton;
    img: TImage;
    procedure showImage(sender: TObject);
  private
    { private declarations }
  public
    { public declarations }
  end;

In the var section:

var
  frmTest: TfrmTest;

  imagesArray: array[1..2] of String = ('blue.jpg', 'red.jpg');
  buttonsArray: array[1..2] of String = ('btn1', 'btn2');

The implementation of your event:

procedure TfrmTest.showImage(sender: TObject);
var
    i: integer;
begin
    for i := low(buttonsArray) to high(buttonsArray) do
    begin
        if (buttonsArray[i] = TButton(sender).name) then
        begin
            img.picture.loadFromFile('your images directory path here' + imagesArray[i]);
            break;
        end;
    end;
end;

In the Object Inspector, you need to set the OnClick event of your buttons with the showImage procedure.