A Facebook group has various uses. It can be used to publicise your cause or organisation or to discuss a certain subject or just to have some fun (some Facebook groups are rather silly).
There are some things you're not really supposed to do on Facebook but enforcement seems rather lax. For example one of Facebook's more controversial foible's is photos of breastfeeding. Yet it took me very little time to find several groups that included these. Oddly, I couldn't find a explanation of the rules. There's a message on the bottom of the page for creating a group that they don't allow groups that promote hate. Although I generally agree with the objective here, I can see logical problems with this. For example, women aren't normally allowed to become Freemasons so it could be argued that any feminist group automatically promotes hatred towards Freemasons. I don't know how this works in practice.
Obviously the first thing to do is to get a Facebook acount, if you don't already have one. These are free and easy to set up.
Go into your Facebook account and click on the Groups button (this tends to move around when they change the layout). Here you will see the groups you belong to listed and maybe some that people think you should join.
At this point you should think of what sort of group you want to create. Think of the most descriptive title. This is not a time to be imaginative. If you want to discuss Queen of the night cacti, choose a name like "Queen of the night cacti" or "Selenicereus" (the Latin name - OK this gets a bit complicated but that's not relevant here)not "Loving by Moonlight".
I think there's a problem with redundancy in Facebook groups (e.g. "Cactus & Succulents", "Cactus and Suculents ", "Cactus & Succulent Society", "Collectors and Traders of Cacti and Succulents " - there are some groups for subsets of cacti and succulents etc. - I'm not sure this is a complete list), presumably a single group would have more members and activity and be easier to monitor. Therefore before setting up your group, you should make sure there isn't already one that meets your needs. Try typing relevant words into the search box and see what comes up. You will probably get things in addition to groups at first so click on "Show all groups". Hopefully you'll know a lot about the subject you're setting up a group for so you will know related terms. By relevant words, I mean words people are likely to use in the title of a group similar to the one you want to start. For Queen of the Night Cactus try "queen of the night" - this gives a bunch of things mostly not about cacti. "hemiepiphytic cacti" gets nothing. "selenicereus" gets several groups including "Dragon fruit" (produced by Queen of the Night Cacti). Anyway you're probably setting up a group about your band or antique furniture or something. If there's already a group very similar to the one you want to set up, it might be an idea just to join that.
If you still want to set up a group, click on the "Create a Group" button. This will bring up a page with a form and you just fill in the fields. When you've done this, click on "Create Group" at the bottom of the page. Another form comes up with a lot of things you can change, like who can write on your wall or upload photos. Set this according to what you want.
Then you can invite people to join, write messages on the wall, start discussions etc.. One of the first things you'll probably want to do is upload a photo for the thumbnail. This is so user-friendly it can be hard to figure out. You just click on the question mark where you expect the graphic to be and select "Upload photo" from the options, then just upload in the normal way (I assume you've created a suitable graphic first).
Well that's really it. You can change pretty much anything if you have problems.