I've never tried it yet. You can't touch the official cube but can with with another one, correct? I'm assuming you know the scramble.
So, here's how it goes: everyone sits down at a table. Each person can bring up to 3 of their own cubes. Everyone gets a piece of blank paper and a pen (or you bring your own pen).
Everyone is also given a piece of paper, face-down, with a scramble written (and drawn) on it. When the time starts, everyone turns their paper over (like a school exam) and starts. You can do whatever you want (within reason!) during the hour, but at the end of the hour you are expected to hand in a piece of paper with a solution written down which solves the cube for the scramble you were given.
Obviously, you start by scrambling one (or all) of your cubes, and then you get on with solving it, writing down your solution as you go, on the scrap paper. Typically you try out a number of possible approaches before finding one you like, which you polish off, check carefully (by trying it on the scrambled cube) and then write down to submit as your solution.
You have to use the right notation (e.g., Rw, not r). You can write down rotations (x, y, z, x', y', z', x2, y2, z2) but they don't count as moves. It's an extremely good idea to learn to do the solving without rotations, though, as it is really easy to make a mistake if you use rotations in your solve. M moves count as 2 (and also E and S, of course), but it's better to avoid them altogether and use, for example R L' instead (this is because it can be helpful in finding cancellations -- e.g., maybe you do an alg that ends with M, and is then followed by another algorithm that starts with R'. That R' cancels with the R and you're left with two fewer moves.
There are a few other nuances -- e.g., you're allowed to put little stickers on your cube(s) during the solve, to help with inserting commutators, and your solution
has to be 70 moves or fewer -- but otherwise it's pretty straightforward, and a lot of fun!
If you want to get serious with FMC,
this guide is awesome and tells you absolutely everything you need to know, including the most advanced stuff (e.g., NISS).