In later versions of Access you can use the FileDialog property of the Application object.

Here is an extract from the MSAccess help file:

Using the FileDialog object
Use the FileDialog property to return a FileDialog object. The FileDialog property is located in each individual Office application's Application object. The property takes a single argument, DialogType, that determines the type of FileDialog object that the property returns. There are four types of FileDialog object:

Open dialog box - lets users select one or more files that you can then open in the host application using the Execute method.
SaveAs dialog box - lets users select a single file that you can then save the current file as using the Execute method.
File Picker dialog box - lets users select one or more files. The file paths that the user selects are captured in the FileDialogSelectedItems collection.
Folder Picker dialog box - lets users select a path. The path that the user selects is captured in the FileDialogSelectedItems collection.
Each host application can only instantiate a single instance of the FileDialog object. Therefore, many of the properties of the FileDialog object persist even when you create multiple FileDialog objects. Therefore, make sure that you've set all of the properties appropriately for your purpose before you display the dialog box.

In order to display a file dialog box using the FileDialog object, you must use the Show method. Once a dialog box is displayed, no code will execute until the user dismisses the dialog box. The following example creates and displays a File Picker dialog box and then displays each selected file in a message box.

Sub Main()

    Dim fd As FileDialog                                                    'Declare a variable as a FileDialog object
    Set fd = Application.FileDialog(msoFileDialogFilePicker)  'Create a FileDialog object as a File Picker dialog box.

    'Declare a variable to contain the path of each selected item. Even though the path is a String,
    'the variable must be a Variant because For Each...Next routines only work with Variants and Objects.
    Dim vrtSelectedItem As Variant

   
    With fd                                                                       'Use a With...End With block to reference the FileDialog object to loop thru multiple files.

        'Use the Show method to display the File Picker dialog box and return the user's action.
        'The user pressed the action button.
        If .Show = -1 Then

            'Step through each string in the FileDialogSelectedItems collection.
            For Each vrtSelectedItem In .SelectedItems

                'vrtSelectedItem is a String that contains the path of each selected item.
                'You can use any file I/O functions that you want to work with this path.
                'This example simply displays the path in a message box.
                MsgBox "The path is: " & vrtSelectedItem

            Next vrtSelectedItem
        'The user pressed Cancel.
        Else
        End If
    End With

    'Set the object variable to Nothing.
    Set fd = Nothing

End Sub