Please note that if you use a wax, you are not actually removing the swirls, but just filling them in to make them less visible. If you really want to remove them a fine polish is needed and an orbital buffer. You can try it by hand, but usually you end up putting more swirls in due to uneven pressure and speed by your hand. Zaino makes a great fine polish that was just released that is excellent on swirls, also you can use 3M swirl mark remover for dark colored cars. Griot's Garage has a fine polish that I have seen work well too.
The key is really to use an orbital buffer and the proper pad or a rotary buffer. I would only recommend using the rotary buffer if you have experience, otherwise heat can build up with this buffer and you can burn through your paint. Heat will not build up with an orbital buffer.
Hope this helps.
Kurt