These are basic guidelines for fitting ships. These are not rules: Eve University only uses rules about what modules you can fit and which ships you can fly during wartime. (Note that although they only apply during wartime, they are strictly enforced when they do apply. You can find them here.) Unlike the rules about wartime fitting, these are just guidelines. They are designed to help you until you know when you can ignore them.
Fit for a purpose
Generally, the more tasks you want a fit to do the worse it performs at each particular task. Some ships have very specific uses: a Bantam (the Caldari mining frigate) is not very helpful in either pve or pvp combat. But even a combat ship will almost certainly need different fits for pve and pvp, because, for example, in pvp you usually receive a lot more damage in a much more limited time than in pve, and enemy players, unlike npcs, need to be prevented from warping away. Even within pvp the same ship can have one fit for close-range brawling in a small gang and a completely different fit for fighting at longer ranges in a large fleet.
Of course, there are dangers in over-specialisation too, especially when you're not working with other players. If you're going to exploit a low-class wormhole while solo you want your ship to deal and tank damage, launch probes, and maybe cloak so that you can hide if you see a gang of enemies on your directional scanner.
Consider your ship's bonuses
Every ship comes with per-level bonuses, which often point towards the uses that the ship was designed for. The Caldari Blackbird, for example, gets a 15% bonus to ECM Target Jammer strength and a 10% bonus to ECM Target Jammer optimal range for each level its pilot has in the Caldari Cruiser skill. These bonuses suggest that it's best fit as an electronic warfare platform which fights well at long range. Sometimes it's okay not to take advantage of a ship's bonuses: the Amarr Punisher frigate, for example, is sometimes fitted with projectile weapons rather than lasers because it has a cap use bonus for lasers rather any damage or rate-of-fire bonuses -- and projectile weapons don't use cap anyway. Generally, however, you should work with your ship's bonuses.
Don't mix tanks
If you're going to tank (and not all fits include a tank) either shield tank or armor tank. Don't shield tank and armor tank in the same fit. Most of the time a tank takes up a substantial proportion of your powergrid, your CPU and either your midslots (for a shield tank) or your lowslots (armor tank). If you fit a shield tank, you can put useful things (damage modules, speed and agility modules &c) in your lowslots, and if you armor tank you can put useful things (tackling modules, electronic warfare modules, propulsion modules &c) in your midslots. If you mount two tanks, even if they're both buffer tanks, your ship won't be very useful except as a target.
Don't mix guns
If you have a rack of exactly identical guns on your ship, they will all have precisely the same optimal and falloff ranges, and exactly the same tracking. This means you only have to worry about getting your ship to one ideal range and keeping the enemy's angular velocity below one value. Furthermore, you can group identical weapons so that they can all be activated or reloaded or unloaded at once, which reduces the micromanagement required in combat. Grouping isn't always the best option, especially if you learn to overheat your guns using the Thermodynamics skill, but it's a good way to start. (There are, however, cases where having mixed guns due to fitting reasons can squeeze a bit more DPS from your ship.)
Missiles are a little different, because they aren't affected by tracking and have a simpler kind of range, but the same principle often applies to them. Note that 'don't mix guns' doesn't mean you shouldn't put missile launchers in extra highslots if all your turret hardpoints are full and you want more dps (as in, for example, a Rifter with three autocannons and a missile launcher) -- though there are other options for spare highslots, such as neuts/NOSes, salvagers, tractor beams, remote repair modules and drone link augmentors.
Bigger guns are not necessarily better
Bigger guns do more dps, assuming they hit, but they track worse and they use up more powergrid and CPU. So, for example, there are three kinds of medium-sized autocannon (the short-ranged kind of projectile weapon): dual 180mm, 220mm and 425mm. The 425mm autocannons do a bit more damage, but the 220mm autocannons have much more forgiving fitting requirements (especially if your fitting skills -- see below -- need more training). On some ships it may be that fitting a rack of 425s would use up so much powergrid and CPU that you wouldn't be able to fit a tank. In that situation, fitting 220s would be better because, even though you would do a little less damage per second, your ship would survive longer and so apply more total damage.
(This does not mean that you should fit frigate-sized guns on a cruiser. Downsizing within the available medium or large guns is often wise, but downsizing from large to medium guns, or from mediums to smalls, usually isn't, unless you're fitting a bait ship or certain kinds of drone boat fits.)
Try fits outside the game
There are a number of programs which let you try out out a fit hypothetically, outside the game. The most popular is the Eve Fitting Tool, which you can acquire here. EFT can tell you about the performance and fitting requirements of a particular fit. If you import your character's skills into it it can give you numbers accurate for your character. This lets you check that you can fit everything you want on to a particular ship before you buy the ship and modules. EFT's numbers aren't always perfectly accurate, and it's possible to be caught up in the numbers so that you forget the practical realities of piloting in Eve -- EFT can import your character's skills but it can't factor in your own piloting skills and experience. Nevertheless, it's a very useful tool.
Steal other people's ideas
Eve University has a Ship Setups forum where pilots can get comments on their fitting ideas. It has some threads with suggested basic mining frigate fits, basic mission-running frigate fits, basic University pvp fleet frigate fits and cheap frigate and cruiser fleet pvp fits. It's also worth searching the forum for past threads if you're interested in a particular ship.
Within the game itself, if you go to the fitting window, click 'Browse' and select 'Corporation Fittings' in the drop-down box of the fittings browsing window, you can see a limited selection of basic pvp fleet fittings. You can also get advice in the University's chat channels. (To link a fit that you have set up already into chat, drag the ship's name from the fitting window and drop it into the chat entry box; to link one from the fittings browsing window, drag the image of the ship.)
If you want to go further afield there's a forum for Eve players called Scrapheap Challenge which has fairly comprehensive pvp and pve ship fittings forums. Bear in mind that fittings suggested on Scrapheap are usually aimed at players with a lot of skillpoints, and a lot of the pvp fittings are for small gang or solo pvp. It's also a forum with a fairly aggressive and competitive posting culture which doesn't suffer fools, new members or people who break the rules (or any combination of the three), gladly.
There is also Battleclinic.net, which has a popular database of suggested fittings. Treat Battleclinic fittings with caution, however, as many of them are jokes, attempts to troll, or just plain bad.
There are some low-slot modules which increase your powergrid or CPU. Co-processors increase your CPU by 7%, and Reactor Control Units increase your powergrid by 10%. There is also the Micro Auxiliary Power Core, which is designed specifically for frigates: rather than giving a percentage increase to powergrid, it gives you a flat increase of fifteen MW. Finally there's the Power Diagnostic System, which increases your powergrid by 5%, and also gives bonuses to your shields and capacitor. There are also rigs that can make fitting easier.
It is sometimes necessary to use a fitting module or a fitting rig, but if you have a fit that requires more than one it's often a bad sign, and it may mean that you need better fitting skills.
Fitting skills reduce the CPU or powergrid requirements of modules, or just give you more raw CPU or powergrid to play with. Having decent fitting skills is very useful, and having very good fitting skills really helps to fit T2 modules and weapons, which demand more CPU and powergrid than their T1 equivalents. Levels in these skills are often required to fit useful modules, too. The fitting skills are:
- Electronics: 5% more CPU per level
- Engineering: 5% more powergrid per level
- Weapon Upgrades: 5% less CPU need for weapons per level
- Electronics Upgrades: 5% less CPU need for signal amplifiers, co-processors &c
- Energy Grid Upgrades: 5% less CPU need for most of the modules listed under "Engineering Equipment"
- Shield Upgrades: 5% less powergrid need for shield extenders, shield rechargers &c
- Advanced Weapon Upgrades (requires Weapon Upgrades V): 2% less powergrid need for weapons per level
(Note that Hull Upgrades doesn't make fitting easier, even though it has 'Upgrades' in its name. It gives you 5% more armor per level -- still great, but not fitting-related.)
For more detailed guidance on fitting a tank, see the shield tanking and armor tanking wiki pages. You can find the restrictions on ships and modules during wartime (already linked in the opening paragraph) here. During wartime pilots who wish to fly battlecruisers or battleships must be able to fit a T2 tank (either armor or shield); the skills required to do that are outlined here.