Facebook Groups
It is fully possible to drive lots of targeted traffic from Facebook groups. The hard part is to make sure that you are not coming off as a douche that is just trying to make a buck. You want to make sure that the content you share is relevant and useful for the members of the group. You also don’t want to share your link with everyone in every single comment you do.
This means that you will need to be social and active in the group(s). I would say that you can link your page in maybe 1 comment out of 8- 10. So if someone see that you post a link they can’t accuse use of spam because it is a onetime thing (for now lol).
You want to join as many groups in your niche as possible and then be active in all of them. It is time consuming but that is something you will have to deal with.
Many times, the group rules forbid you to post any links at all. That will require you to be active and helpful in the group and make sure that people notice you and when they do they are curious to find out who you are and will click on your name to go to your profile. Over there, you should have a link to your fan page or landing page (fan page is often better). You can have a link to it in the employment sign, the cover photo, a featured photo, your about section etc. I think you get the point.
Facebook groups are very time consuming and there is no guarantee that you will get any traffic at all. You should not rely on Facebook groups as your main traffic source.
HOWEVER
If you are hanging a lot on Facebook and you are a member of many groups that is relevant to your niche, then you should of course take advantage of it.