Preface: The most recent resource I played was this digital release on drivethru rpg (2010). I like the game and would play it again.
There are some things to know about Tales from the Floating Vagabond (Vagabond, from now on).
Vagabond is not a serious game
You probably already knew this to some extent, but you need to make sure your players know it. Power Gamers are gonna have a bad time.... or make it so that you do. Everyone needs to be on the same page about how this is going to go. You can do weird things with the race builder that may or may not be intended and make 3.x D&D's dump stats look well balanced.
I cannot reiterate this enough
Everyone should be on the same page about playing this. It's a goofy, fun time with any character you can make; those things do not make a streamlined and rules-sensible experience. No one wants to do a full session-zero for a 1-shot (and I'm not recommending it), but politely remind your players that this is more of a "beer and boardgames" kind of night.
Vagabond is a bit loose with the rules
I'm loathe to disservice Fate by comparing the two games, but there's a certain "fly by the seat of your pants" quality to Vagabond that I observed from myself as a player, the other players, and the gamemaster. Things are going to come up that don't mesh well with the rules and the players are going to frustrate you. This goes back to the previous point: make sure everyone knows that Vagabond is not a super crunchy game like D&D.
What do you need to read?
You need to skim the whole thing; the chapters all have silly names (Getting Schticky or How to Deal with Antisocial Behavior), so I'm just going to use numbers.
Depending on how much you're helping the players create their characters (usually a lot), then the first 4 chapters are more or less important.
Chapter 7 is all about combat so you're going to need to have a pretty firm grasp on that. This is probably the chapter you'll need to read the most times.... not counting rereading sections of character creation so that you can help Bill finish up his Rick & Morty - unicorn slayer crossover.... again.
Chapters 8 and 9 are more resource than content. Chapter 9 actually has npc stat examples, so bookmark that.
Chapter 10 is actually a sample mini adventure. If you want to run it, tell your players not to read it. If you can't trust them, then only give them chapters 1-4 and maybe 7.
The whole book, including pictures and charts, is a little over 100 pages. You should be able to peruse the whole thing over your lunch break and get a pretty firm grasp on everything else in a few hours.
What do the players need to read?
In short, Chapters 1-4 and maybe 7. Chapters 1-4 cover characters, creation, and their stuff. There are 8 attributes instead of D&D's 6 and I had to read what "cool" did about fifteen times.
Character creation is as hard or as simple as your players want it to be. The game has a few pregens, and also rules to completely make new species. As mentioned earlier, you're going to want to encourage power gamers not to go overboard with species creation, because it's pretty exploitable.
That said, character creation (including reading) should take under 2 hours for even the most discerning gamer, and likely under 1 hour.
The game uses dice of varying sizes to differentiate difficulties. Difficulty Level is defines in the glossary (and no where else that I can find). You're trying to roll under your score; 1d4 for easy stuff, 1d6, 1d10, 1d20, 1d30 (yes, d-thirty), and up to 1d100 for things that are nearly impossible. If you want to use only physical, real world dice, double check your collection.
I recommend that you have everyone send you their characters to look over ahead of time, preferably with 1-2 paragraphs about who they are and how they made their way to the Floating Vagabond. This is partially so that you can fact check them, and partially because character creation isn't great and you don't want half the party doing it on the fly at the table.