In your stylesheet, you need to create those styles (blockquote.left , blockquote.right) and whatever attributes you want. In your MODx settings, you need to tell TinyMCE to show those styles in the drop down:
In the System > System Settings page, find the ’Filter by area...’ dropdown. Change ’core’ to ’tinymce’ and look for the css selectors settings. Add your styles there.