What do you need in order to organize a chess tournament? We have a small local chess club group on Facebook and chess.com, and we want to organize a small event where all the members can play against each other. We will ask players who play for the national teams to join. If they do, it's going to be big, and therefore I need to organize it in a decent way.
There are 5 admins for the group. One is me, two living abroad and can't make it, another one who can't make it because of some other reason, and the fifth isn't active. I don't know if he's alive, to be honest. :)
So from the looks of it, it seems as though I will be responsible for organizing it. I might ask some members to help me since I'm disabled. I haven't joined any chess clubs because they are too far from my home, therefore I have basic questions.
These are my questions.

Do you buy chessboards for the players? Or, are the players responsible for getting them? If so, what happens if a player doesn't bring his board with him? And if it's my responsibility to buy boards, how many should I buy? Half the number of the participants, or a board for each one? What about the quality of the boards? Do they have to be made out of wood or decent plastic or would anything do?
Do I have to buy the score sheets? Or, are they not important for small friendly events?
Do I have to divide them into groups? What if I don't know their Elo? Do I let them play each other randomly 2500 vs 1200 Elo? :) or do I ask for age?
What is the ideal location? An internet cafe? a restaurant? or should I ask a local chess club to open the doors for us for 1 event, maybe that way, the boards, and everything will be ready. But what if they refuse, what's the plan b, outside of a chess club?
How many trophies are there usually? 3? I want to know so I can buy them.
Should I play or should I just be an organizer? What if there's a problem? Should members play the roles of arbiters, when they are not playing?
Is there a question I should have asked and didn't? Did I forget about something? Anything else I need to know?

Edit: I ust want to say that the vice president will take care of some details indicated in the answer below.
A few things should come first, others can come later.

One, what type of event do you want to run? Several of the later questions depend on how formal the event is going to be, and people need to know what kind of an event it will be before they know whether they want to come at all. You have zero experience and mention the word casual, so we'll go for very casual, fun, not formal at all.

Two, how many people can you reasonably expect? You need to know a minimum number (if fewer than this number of people have registered a week before the tournament, we'll need to cancel), and a maximum (we can't accommodate more than this number of people). This ties in with important question three.

Three, how long do you want it to take. Will this be a whole day tournament, only an evening? Are you thinking of blitz, or rapid, or standard? If it's standard, you can only fit one or two games into an evening, but a whole blitz tournament easily goes. The time control that most says "fun and casual" to me is 10 minutes per game.

Four, the venue. This differs by type of event (we're casual), and before you start looking for one you need to know roughly what size you want, and after you've arranged it, this decides the min and max people. You'll also need a very different venue if you want it for one day or for the evening. I would definitely contact the local chess club, because hey, they're the local chess club! They might even enjoy helping you out with all this stuff for fun (in my country anyway, these are purely amateur organizations doing chess stuff as a hobby). Other than that, when I think casual chess tournament with people I know from the Internet, I think lots of beer. Look for tables in local bars, or event rooms at local bars, that sort of thing.

You'll also have a date by now.

So now you can tell people, "We're doing a fun and casual, 10 minute / game rapid tournament, unrated, time X on date Y in venue Z. Please register if you want to come!"
No, wait, you can't -- you don't know yet how much it's going to cost!

Let's talk a little bit about systems. Formal competitive chess tournaments often apply the Swiss System. It's very fair, you play against people who have the same number of points as you have, you get more or less equal numbers of black and white, and often the best players wins. It's a nightmare to run correctly, mainly because you have to get all the results after each round, enter them all correctly into the computer (or do it by hand, let's not) and then print out new pairings and find out something has always gone wrong. And even if it goes perfectly, people have to wait until the last game of the round is finished all the time.

Let the players do the work. For groups up to around 10 players or so where everybody plays everybody, there are "Berger tables" with pairings for each round: http://www.tournamentdirector.co.uk/berger_pairings.html . Show the players the pairings table, and let them fill in the results on a form you have printed out beforehand. No work for you during the tournaments.

If you have too many players (too many rounds for the time you have the venue), there's the Amsterdam System: first put players in small groups, of 4 or 6 people. Make one player the leader of that group, and give him a form for it. Let them play a little subtournament. When all subtournaments are done, make a ranking of all the players based on the points they got, then make new groups based on that. A finals group with all the best players, second group with the second best, etc. The key is that during most of the tournaments, the players are doing the administration and it all goes a lot faster.

Oh yes, your questions:

Chessboards: You're not going to become a chess club, are you? Try to borrow some from the chess club, and otherwise let people bring their own. Let them bring clocks, too! White player has choice of set.

Buying score sheets: Not necessary in an informal rapid tournament.

Dividing into groups: Not necessary in an informal rapid tournament (and in the Amsterdam System, they end up in the right group soon enough anyway).

Location: mentioned some things already.

Trophies: More is always better. Prizes can be silly things, I've won Tupperware stuff at great chess tournaments. Bottles of wine always work well as top prizes, but the golden rule is that more than half the people should go home with at least a tiny something. Besides the obvious best junior, best female, best organizer, prize for the guy who came last, prize for the guy who came second to last and expected he didn't have to come up and collect a prize, player whose performance was least noticeable, etc etc. Prize givings like these are great memories for everyone, and any other kind is instantly forgotten. And don't do money prizes, you're a casual tournament.

Play yourself: You can, but you better have everything for pairings and results exactly planned out, and it's going to be hectic. Playing arbiters: formal arbiters aren't necessary in a purely informal tournament without money prizes, but if there are any actual arbiters or very experienced players in your group, that's very helpful to know. Make them the Committee of Appeal and let them handle people who argue.

And now I need to sleep. HTH.

(I still don't know about the cost. It's venue + prizes / number of players, but if the venue cost is fixed and you don't know the number of players, you have to fiddle it to prevent too much risk for yourself)

(Addendum: and don't do this alone. Some assistants when it gets all hectic are needed)