How can I set the current page of a TPageControl?

Add a button to the form and write an OnClick event handler like this:

procedure TMyForm.Button1Click(Sender: TObject);
begin
  PageControl1.ActivePage := TabSheet1;
end;

You can use ActivePageIndex:

procedure TForm1.Button1Click(Sender: TObject);
begin
  PageControl1.ActivePageIndex := 0;
end;