With Inno Setup how can I rename and copy a file a user chooses (an image) to the program files directory

How to create a filtered input file wizard page item ?

For the purpose of file selections you should use a separate input file wizard page, which you can create by the CreateInputFilePage. Then, the Add method of the TInputFileWizardPage page object class contains the AFilter parameter where you can specify the filter for files that can be selected by its associated file open dialog. In this example we allow the users select only *.jpg files:

[Setup]
AppName=My Program
AppVersion=1.5
DefaultDirName={pf}\My Program

[Code]
var
  InputPage: TInputFileWizardPage;

procedure InitializeWizard;
begin
  // create the input file wizard page
  InputPage := CreateInputFilePage(wpWelcome, 'Caption', 'Description',
    'SubCaption');
  // and insert one item in which the user will be restricted to select
  // only *.jpg files
  InputPage.Add('Prompt', 'JPG files (*.jpg)|*.jpg', '.jpg');
end;

How to manually invoke a filtered file open dialog ?

If that input file wizard page doesn't fit to your design and you want to make your own, then you need the GetOpenFileName function to show an open file dialog. Even this function contains a parameter where you can specify the filter string. In this case it is the Filter parameter. In this script example is shown, how to invoke a file open dialog with a *.jpg file filter:

[Setup]
AppName=My Program
AppVersion=1.5
DefaultDirName={pf}\My Program

[Code]
procedure InitializeWizard;
var
  FileName: string;
begin
  if GetOpenFileName('Prompt', FileName, 'C:\InitialDirectory',
    'JPG files (*.jpg)|*.jpg', '.jpg')
  then
    MsgBox(Format('Selected file: %s', [FileName]), mbInformation, MB_OK);
end;

How to build a filter string ?

As you can see in the above code, the filter string consists from the caption part and the filtering portion separated by the | char. You can also specify multiple filters by separating each filter string, again, by the | char, or you can specify multiple extensions for a single filter by separating extensions by ;.

So, e.g. to create a filter named JPG files filtering only *.jpg files you can write:

JPG files|*.jpg

To make two filters, let's say one for *.jpg files and one for *.jpeg files you can write:

JPG files|*.jpg|JPEG files|*.jpeg

And finally, to make a single filter for *.jpg and *.jpeg files you can write:

JPEG files|*.jpg;*.jpeg

For details I would refer you to the Delphi reference page for the TOpenDialog.Filter property.