Fitting in EVE can be an art, and your choices while in eve isk station can make or break the outcome of a trip around the EVE-verse. However, before you venture out and become the Michelangelo of ship fitting, it can't hurt to learn some basics. At first, the choices seem overwhelming and it is easy to become confused, but once you understand some basic mechanics, the mist starts to lift. One thing to bear in mind is that there are only a few absolute limitations to what you can fit on your ship. Beyond that we enter into the realms of "good" and "bad" fittings as well as "usual" and "genius" approaches to it. So let's get started with some hard facts.
Every ship that can be fitted has slots. These are high, mid, and low slots, as well as rig slots. Some have a drone bay. If you look at the info window of a ship, you'll find the size of the drone bay in the Attributes tab. With the correct skills, you have the ability to use up to 5 drones at a time on non-carrier class ships, but can take more than that in your drone bay if the size permits.
Slots can be seen in the Fitting tab in the ship info. To find out whether you can fit a module on a ship, you need to check the Fitting tab in both the info of the ship you want to fit and the modules you want to use. You can see the slots available on your ship if you open the fitting screen when docked in station. As you will notice, ships have eve isk Hardpoints. Those can be Turret or Missile Launcher Hardpoints. The limitation is that you can fit only as many missile launchers as Missile Launcher Hardpoints are available, and the same is true for Turrets. Mining lasers count as turrets, so you can't fit those on a ship that has only missile launcher Hardpoints. There are modules that fit in high-slots, that don't require a Hardpoint, like a Nosferatu. Such modules can take up high-slots that don't have a Hardpoint as well as those that have Missile Launcher/Turret Hardpoints.
There are some ideas about fitting ships in EVE, which you can either follow or choose not to. As you noticed, each race builds its own ships. The key is that every race has its preferences on how the ships should be used to achieve the best results. Let us take a look at them one by one.
Amarr ships are heavy tankers and Amarrians prefer an armor-tank. They mainly use turrets, energy weapons, which come in the variations "Pulse Laser" and "Beam Laser". These weapons use a lot of capacitor, which is reflected in the build of Amarr ships.
Caldari ships are known for shield tanking and use a mix of missiles and hybrid eve isk weapons for offensive purposes. These come in the variations "Blaster" and "Railgun" and they make use of some capacitor, although not as much as energy weapons. Finally, some Caldari ships are pretty effective with Electronic Warfare, in particular ECM, which allows you to prevent another ship from firing back by jamming its weapons.