I'd assume that's an important issue to address, Quirky.
Australia is 14 hours ahead of New York and 18 hours ahead of California (although, going backwards, Cali will get a better connection since they only have a time difference of 6 hours rather than 10 hours).
So...
First things first: Designate a Tourney Organizer (TO).
If the plan was to do Round Robin style playing (where everyone plays everybody):
-Everyone needs to post the times they will be available to play, or PM or VM that to the TO.
The TO needs to:
-Find the difference in times and make a table of when everyone's times to play match up.
-Set up matches between people, determining the best way to match everyone up so that everyone gets the best chance of being able to play everyone else.
-PM, VM or simply post the tourney matchups here. Be aware of the difference in time zones, and if PM or VMing the matches be sure to write the times of matches according to the time zone of the person you are writing to. It might be a hassle for the TO to figure everyone's time zones out, but it will be a bigger hassle when people try to figure out the time zones for themselves and mess up the times they are able to play each other. At least if the TO makes a mistake and someone figures it out beforehand, the TO can post a notice to everyone to adjust their TO-synchronized playtimes ahead or behind a couple of hours rather than trying to help every individual person try to confirm that their calendar of times to play is correct.
-Set up any specific rules that you want the tourney matches to be set by, such as number of games played per person (such as best of 3). Keep them simple and short; people may only be able to get on WiFi for 15 minutes before getting back to something else.
When tourney day comes, everybody needs to:
-Keep Xat open whenever you are online.
-Be flexible. Everyone has a lot of stuff to deal with IRL, so getting impatient when people need to change times is Be aware that schedules are tentative for everyone and subject to change; this isn't a massive, rule-bound tourney: You are here to have fun playing each other and should carry the pleasant, relaxed attitude into setting up matches and not just being friendly while playing the matches. Each person will have one thing or another come up; being nice to others often means they'll be nice to you when you have something come up.
-Adhere to the charts as best as you can. When you and another person you haven't played yet are on, but your match with another player is in fifteen minutes, don't join in with the player who is currently on.
-Off that note, adhere to the chart, but if you can't, try and make a post here that times have changed. Be courteous to the people who are waiting for you--try not to come in at the last minute or 2 hours later and say, "Sorry I couldn't make it." Be early with letting people know rather than late. The people waiting on you are real people, sitting boredly at their computers, waiting for you to be polite enough to let them know something is up. If you can't make it, make it easier on them and let them know that they can be getting something IRL done in the meantime, too.
The TO needs to:
-Be ready to add all point totals up. As each individual will have known this was just for fun, showing how each person fared against the others is probably the funnest part of the tourney. Each person will be terrifically excited and want to talk to each other about all their matches and speculate about how other people's matches went, how they played, and any other particulars. Hashing out the details between other people's fights is a lot of fun for the new players, and discussing particulars of their fights with the new players and showing them how things went is a lot of fun for the veterans, too. Post those results and let people talk about this tourney and how fun it was for a long time. This also has the added bonus of helping people discover where their chinks and flaws are. A player might notice a surprising loss from another player and be intrigued enough to ask. Together, they take note of something that the original player hadn't realized was a flaw before and they both progress while also building bonds.
Remember, this tourney is about:
-Building bonds. You're getting to know your fellow board members and therefore becoming more enabled to post meaningfully on the discussions on the forums. People will be able to see flaws and strengths in your arguments after playing you and having learned a little better where you are coming from to be able to contribute to the boards.
-Having fun. No one's determining the best Link; heck, this is WiFail. Discrepancies and random losses that should not have happened under any normal circumstance are the norm for WiFi and should be laughed about. Not a single competitor cares about how it was your fingers that slipped and caused you to SD and how if you hadn't then you would have had the most terrific KO opportunity ever. Everybody around you, no matter how skilled, made a lot of slip-ups too. The only difference is they know to laugh about it because it is so common that it is inconsequential. Lighten up and laugh, because that's the main purpose of the tourney.
-Becoming better players: Some of us are limited to WiFi; some of us are hoping to become top dogs in our regions; some of us are here just to get a taste of what competitive Smash is like and maybe make some friends in the process. Serious critiquing can be saved for another circumstance, but a little bit of "You should try to avoid rolling into my smashes" or "just mash up and you'll get out of my jab combo" never goes amiss. We all like having fun and improving at the same time. Compliment on what your competitors are doing right and give a little boost up on what you notice they're doing wrong.
-Showing respect: You're respecting other people here as you play. No matter how disorganized things may get, you're always dealing with other people who want to have fun as much as you do. Their respect will grow for you as you show your respect for them.
I bolded "everybody" and "Tourney Organizer" as well as color-coded them to help figure out who should be adhering to what. Green is for the TO and Magenta is for everyone involved in the activity.
I really hope this helps you guys get a leg-up to making the tourney a successful one. I'll be missing you all.
Of course, feel free to change this, add to it, or tell me where I'm wrong as you like: It's only a suggestion. Good luck!