It was not easy. I tried different methods. The easiest and best way is to use the popular plugin called “Facebook Comments for WordPress” by we8u. The instructions are pretty straightforward. There were apparently a few bugs in the initial few days after FB released the API. But FB has fixed them.
Note that when you install it, even after following all the instructions, you will see strange warnings at random places. This only lasts a few minutes. It happened on both my websites. Look It Up 4 Me, and on this one. I think that once the plugin synced with FB all the errors went away (or may be because I was tinkering with it.) It was easier the second time though.
I have completely turned off the WordPress comments. I also had to disable the other FB like. It was superfluous anyway.
The main advantage of FB Comments is that if the viewer is logged in to facebook, the comments rearrange themselves to be relevant to him or her based on his facebook profile. That is a wonderful experience, compared to static comments in sequence. There may be some disadvantages as well, but lets wait and see what happens.