This guide assumes you already have experience flying subcap (DPS/logi) fleets and will only explain capital specific mechanics, it also assume you have the doctrine required base skills, Jump Drive Calibration V, Jump Fuel Conservation IV, Jump Drive Operation V etc.
You need to join the capitals group before flying in fleets. Joining the group gives access to capitals discord chat, forum, capital mumble subchannels and pings; as well as capital SRP.
While capitals are generally powerful, when isolated they make attractive, expensive targets for a gang of subcaps. One of the ways people can trap you is to fleet warp you away to danger by tricking you into joining their fleet, or using a spy in fleet squad commander position to warp you off and kill you. So to avoid this:
Your capital ship has a jump drive which can instantly teleport you to a cyno in range (7 ly for a capital, 6 ly for a supercapital). Several criteria must be met:
After jumping you will be unable to tether for 30 seconds, which means you can be tackled. Dock quickly to avoid this, this also means you shouldn't cyno your capital onto anything smaller than a fortizar (or supercapital on smaller than keepstar) unless you know what you are doing.
You will have used up a large chunk of your capacitor so you should start capping up as soon as possible, so you are ready to jump out or use your emergency hull energizer (EHE).
Whenever possible, do NOT jump to a Pharolux Cyno Beacon (the anchored upwell structure - aka a 'cyno beacon'). They are always anchored far from the safety of a tetherable structure, and you will be very vulnerable when warping off. Cyno beacons are often camped and many, many unwary capital pilots have died jumping to anchored beacons. To make matters worse, some unscrupulous groups anchor cyno-beacons on common routes and bubble-spam them to catch and kill
With that in mind, it is HIGHLY recommended to add the cyno-character to your watchlist, and jump via right-clicking on the name, then clicking 'Jump to Member'. This avoids the mistake-prone capacitor-menu's Jump-To sub-menu - this menu has all available cyno-beacons in range. If you are lighting a cyno for others - typing 'CCCC' in fleet-chat is a common way to identify yourself as a cyno.
If you cannot light your own cyno via a Recon cruiser, you can use a Mobile Cyno Beacon: https://everef.net/type/57319
Dreadnought have the Siege Module, faxes have the Triage Module (and rorquals have indy core but whatever). These use strontium clathrates to activate and immobilize your ship (preventing travel, warping, jumping, cloaking, docking etc) and prevent remote assistance (you can't be repped or receive capacitor transfer) but in exchange your local active rep gets boosted and your outgoing dps and reps get boosted. Because of these downsides FC will tell you when to siege (siege green) and when to exit siege (siege red).
It is important when you first jump in to wait until your speed is lower than 10 m/s before sieging. If you bump and siege, the increased mass from sieging will mean you maintain that speed quite well and you will drift significantly.
Your ship has a special cargo bay called a fleet hangar, this bay is private to you by default but can be opened up to fleet members or corp members by clicking the little buttons next to the hangar. This is where you can keep things like cap boosters or refits, you probably want to keep it closed to prevent thieves and only open it when needed.
Similar to the fleet hangar the SMA can also be opened to fleet or corp members. This bay can be used to store and jump into fit ships. Possible uses cases include storing spare ships for fleet members to reship into, moving ships for move ops or carrying ammo/charges/strontium/heavywater inside industrials.
Additionally the SMA (even when closed) provides a fitting service like mobile depots to fleet members <5km away. So if you are close to another capital in fleet with you, you can refit your ship in space (see useful refits below).
In the event of a loss the SRP payout assumes you fully insured your capital, which can mean a ~300m loss if you do not insure. Insurance is actually quite simple, you get a base insurance payout which you get even for not insuring, and if you pay the optional premium insurance, you get back double what you paid if you die before the insurance contract (3 months) runs out. So it boils down to.. do you believe your chance of dying in the next 3 months is >50%, if so, insuring is worth it.
The reason this is complicated is because if you don't happen to die in those 3 months you have just thrown 300m away, many veterans will tell you about all the isk they've wasted insuring capitals. It's essentially a bet, and you need to make that call depending on the fight you're jumping in to, what ship you're in, how active you are planning to be (and how many capital fights you expect in the next three months) etc etc. However don't just insure a capital as soon as you buy it, wait until there's a fight and you undock.
For bomb dreads (Moros especially, Phoenixes not as much) and faxes in a big capital fight it is usually worth insuring (and FC will probably remind you). One trick to ensuring you insure, is to load up the insurance window and drag it on top of your undock button so that when FC calls for undock, you don't forget to insure.
Carriers generally don't die as often, so that call is up to you.
The dreadnought is the damage-focussed capital class. The Bomb dread is a buffer-tanked short-range anti-capital damage dealer dropped right on top of the enemy while the Sniper dread is similar but uses long-range guns and is used at range against capitals (or perhaps battleships). The HAW dread is an anti-subcap dread with a modest active rep tank.
Often dreads do not get into the fight which is why it's suggested to use dreads on alts, while you have a character flying subcap in the main fleet.
Faxes (Force Auxiliary) provide capital reps to both capital and subcapital friendlies alike. Fleet fax (buffer fit) are used when the enemy are expected to bring capitals while master fax are used when the enemy is expected to bring subcaps or only a few dreads. Typically the master fax are used if they can tank what the enemy is likely to bring, typically subcap vs subcap fights, while fleet faxes jump in to rep against capitals.
Carriers provide fighter support, which are basically suped up, very long range drones. They have their own control system so you should familiarize yourself with them, that is not covered in this guide (yet).
https://forum.pleaseignore.com/topic/84972-updated-capitals-101/
https://forum.pleaseignore.com/topic/100127-so-you-now-have-a-fax-guide/