fotm is short for "fractals of the mists"

Explaining this dungeon-like instance is whole posts on its own, so I recommend looking at the gw wiki article on it.
http://wiki.guildwars2.com/wiki/Fractals_of_the_Mists

The first thing to know from a gear point of view is that there is a new mechanic called "AGONY" and a gear upgrade called "INFUSIONS" that can upgrade gear to mitigate agony (by increasing "Agony Resistance" or "AR" for short.  Infusions are placed in Ascended or Legendary gear.  Your current AR can be found on your character sheet (next to magic find and under crit damage) - but make sure you are looking at it in town or a lvl 80 zone for an accurate count.

For more details on the mechanics, read about fractals, infusions, and ascended gear on the guild wars wiki.

For the first levels of fractals, you don't need AR, but when you get to around fractal 11 you'll be wanting it.  Also, experienced guildies will want to run the highest level fractal you AR will allow, so if you have more AR we can take you to higher level fractals that we might actually want to run

First focus on getting ascended amulet and accessories (20 laurels, 250 badges of honor, 24 guild commendations, and 10 gold per the previous post).

Get 2 +5 agony resistance infusions for your accessories.  Cheapest way to do this is running some low lvl fractals to get 150 fractal relics. If you are absurdly wealthy, you can instead make +5 infusions that also give +5 to one stat. (be warned, these are very expensive, 30+ gold each at current t6 material prices!)

If you plan on running a lot of fractals, then get another 75 fractal relics and buy an infusion for your amulet as well (otherwise get a utility infusion from the laurel vendor e.g. karma, gold, or mf bonus to increase your currency earnings from general pve).

This will get your agony resistance (AR) up to 10 or 15, which should comfortably get you to fractal 20 in guild groups.  However, if you want to run fractals more frequently, you'll need more AR than this for these early stages.  The reason is that experienced fractal runners don't want to do less than ~26, as the rewards just aren't as good (and fractals are not very rewarding in a monetary sense to begin with).  To survive in these groups you really want an AR of 20+.  You may need to help carry less experienced pug groups, and 20+ AR will help you do that (when you miss a boss dodge or in the 4th fractal you won't lose a pile of health).

Unfortunately your options here all cost more money, either cash or lost opportunities.

One option is ascended armor. This usually requires getting the appropriate craft to 500, and having a small fortune in materials. After you make each piece, you can slot a +5 infusion in it.

Another option is an ascended back, which you then upgrade to unlock a special infusion slot to further increase AR. These can be crafted (at considerable expense, requiring a 500 craft and a fortune in materials), or made with expensive t6 materials in the mystic forge (roughly 100g at today's prices).
The final current method is the fractal grind (1850 fractal relics).
But to upgrade it you need 500 more fractal relics, plus a rare drop in fractal 11+.  2350 fractal relics is a lot of fractal!  So if you want to get the jump on AR, sadly gold farming is the way to go (i got a fractal back for my second character, since the first one was able to obtain the necessary fractal relics more readily).  500 relics to upgrade is a much more reasonable number to obtain before fractal 20+.
The point here is that the back alone is good for 10+ more AR on its own, taking you to 20 or 25.  Combining 16 of those +1 infusions that drop in fractals will get you a +5 for the new slot.  You can buy or farm more +1 infusions to be able to make +6-9. Warning: each extra +1 doubles the cost, making diminishing returns kick in at ~+7.  See this topic on the gw wiki for more detail http://wiki.guildwars2.com/wiki/%2B1_Agony_Infusion

Another option is weapons.  But for most classes this is twice as expensive, due to the 2(or more if you swap between fights) weapon sets.  But if you use a single two handed weapon most of the time it can be the most economical choice (one ascended 2h weapon provides 2 infusion slots) .
On a side note, if you already have made a legendary, then go ahead and slot +5 AR infusions in it. Or if you have been lucky enough to get an ascended armor/weapon drop in world events, by all means take advantage of your lucky "free lunch" (assuming the stat combo isn't completely silly for your build).

Finally rings are the last option, and one i do not recommend for this stage. The reason is that rings can be upgraded, but not until your fractal reward level is in the 20s (you can also get them in the final fractal chest already upgraded when your reward level approaches 30+, but the stats may not be what you want).
You can get rings earlier (10 pristine fractal relics, final fractal chest at 11+, or an absurd number of laurels) but any infusions you put in will be lost when you upgrade the ring later.  So while you can infuse them early, you will effectively be wasting 75 fractal relics each.