Eve's attributes do one thing only - they reduce the time it takes to learn skills.
Skills are an important element of an Eve character. In addition to having a benefit (like 5% more damage or some such) they are prerequisite to equipment and ships and serve as the game's "gearscore", a system by which other players will judge you.
The attribute system takes a lot of strategising to optimise. The reason you want to optimise is because people will look at you and go "woo, a 20 million skill point character, he can join our elite corp" as well as to be 5-10% better at killing/mining or whatever you do in the game.
The basics of how the system works are on the Eve wiki so read them through before continuing with this blog post. Be careful though - the article is out of date and the stuff about Bloodlines is redundant and remaps are once a year now instead of once every 6 months. This page is brief but up-to-date.
A downloadable addon that tracks your skill development is available here: Evemon
The way I think about attributes usually is points over the minimum. If you look at Attributes in game in your character sheet window you will get an option to Remap and a display of the points assigned. For each stat there are 4 points in white, you can't move these. You also can't move one of the green ones. So every stat has at least 5 plus whatever you add by training up Learning skills like Instant Recall. The points after this, the ones that can be moved total 14. So you could put 7 in Int and 7 in Mem and be good at learning Int/Mem skills as well as Mem/Int skills. Or you could go 10 Int, 4 Mem and be perfect at learning Int/Mem.
For each skill (full list here) there are two attributes. Add your value for the first attribute to half the second to get a score for how good you are. So if you are 10 Int and 4 Mem you are 10+2 = 12 for Electronics skills. 12 is the best in this system, the worst is 0 which means you put your bonus points in attributes that don't help the skill you're training.
Remapping strategy is all about keeping this number high as it's the main variable. Sure, you learn your attributes skills and place implants in your head but that's kinda obvious and everyone does it. Finessing your remaps takes a lot more thought.
There are four phases to consider with a new character's remaps:
Phase 1: before you remap anything. Train skills that you will need immediately but which don't get benefit from your first remap. So if you plan to first remap to Mem/Int then consider Per, Cha and Wil skills that you may not want to do without for a few months.
Phase 2: first remap. Generally most people are going to want to remap to learning skills. It makes a lot of sense to get your learning skills out of the way early because that way you get maximum benefit. No sense in training up a load of ship skills and then training Spatial Awareness (which lets you learn ship skills faster) afterwards. So I recommend Mem 10 Int 4 or Mem 7 Int 7 or Mem 4 Int 10 for this remap. Go Mem heavy if you want to focus on Learning, Corporation Management, Industry and Drones over Electronics, Engineering, Mechanics, Navigation and Science. It's not a bad idea to keep time down for this phase since it's beneficial to you to get the remap clock ticking by taking your second remap.
Phase 3: second remap. Probably Per/Wil. Everyone needs to learn to fly a range of different ships and most people need to learn weapons. Most combat skills are in this category.
Phase 4: third remap. This is not available until one year after you clicked the second remap button. In fact you may find that you want to stay Per/Wil for a while and get your guns, missiles and ship skills to where you want them before you remap away from Per/Wil. Most 0,0 alliances will expect you to fly a fairly wide range of different ships so check the requirements of some of the corps you are interested in before you remap. For this remap plan a whole year's skills out since it will be a year before you can remap again.
Remember the goal is to be operating as close to a perfect 12 score as you can all of the time.
Here's an example:
New Amarr pvp pilot.
Phase 1. So, what skills are not Mem or Int based and are essential right away? I'm expecting phase 2 to take around 2 months so I will train up some skills I really don't think I can live without. I decide to take Amarr Cruisers to 3 and Medium Lasers to 3 so I can at least shoot a bit. I also like to be able to pick up cheap ships since I expect to get loads blown up so I take Retail and Trade to 2 so I can place adequate Buy Orders.
Phase 2. Mem +4 Int +10 I really want to get my Learning skills out of the way fast so I can get to an impressive skill point total after about a year. There are also a lot of highly useful support skills.
First I get Learning, the low end attribute skills, Eidetic Memory and Logic up as well as Cybernetics for some implants to make it all go faster. (The other 3 learning skills - Clarity, Focus and Presence - are better learned when I'm Per/Wil). Then I grab some of the most useful pvp skills:
Cloaking - if planning on Covert Ops, 1 for the basic cloak, 4 for the better cloak.
Electronics - fit more modules on your ship, really important skill that is quick to get to level 5.
Electronic Upgrades - prereq for many modules as well as Covert Ops ships
Long range targeting, Targeting, Signature Analysis - better locking, worth taking to about 3. Signature analysis 5 is needed for Recon Ships.
Propulsion Jamming - saves cap costs on modules you are likely to be using extensively early on. You need this to 2 for tech 2 warp scramblers and disruptors or 4 for tech 2 webs
Target painting - maybe useful in a dps role, worth a point or two.
E- War skills - probably not good for a newbie because you will get targeted first if you fly an e-war ship. Always going home in your pod isn't going to be much fun early on.
Engineering - fit more stuff on your ship. Worth taking to 5 early on.
Energy Management and Energy Systems Operation - more cap. Take to 3 or 4, you run out of juice a lot early on.
Shield skills - this Amarr pilot can skip
Get basic rig skills for Tech 1 rigs. For Amarr you probably want Armour, Laser and Cap rig capability. Forget tech 2 rigs for now - they're very expensive.
Hull Upgrades is good and is a prereq for many modules including plates. You need this at 4 or 5.
Mechanic - not a useful bonus and not needed as a prereq for basic pvp gear. You can leave this at 3.
Repair systems - don't go mad on this. Early on a buffer tank is much much better than an active tank. This is because generally you will die fast. So having 15k effective hit points is much better than having 10k hit points and being able to repair 5k a minute. 2 or 3 is all you need.
Salvaging - noob cash cow. Level 1 or 2 is fine.
Armour Compensation - very strong skills that add a lot of effective hit points. Get them all to 3 or 4.
Nanite skills - just repair in a station after you overheat.
Everything except the Jump skills is worth taking to at least 3. Evasive maneuvring 5 is required to pilot Interceptors.
Thermodynamics - a key pvp skill. Early on you will almost always want to overheat your modules in your life and death fights. Gives a significant edge.
Cybernetics - 1 for +3s, 4 for +4s (about 100 million isk a full set), 5 for +5s (about 500 million isk a full set).
Astrometrics - get all 4 related skills to 3 or 4 if you want to hunt people down or skip and go straight for damage skills instead. If you go for Covert Ops you should take these skills - your ability to find people and go sit on them will be a key factor in your fleet killing stuff. Many people have separate cov ops alts so they can bring a fighting ship along too.
Before learning Drone skills it's best to learn a few points of Clarity. This is supoptimal for Clarity but boosts your drone learning.
Drones - a number of skills require Drones to a certain level as prereq:
1: Scout Drone Operation.
3: Combat Drone Spec,
4: Durability, Navigation
5: Racial Drone types, Interfacing, Sharpshooting
To taste here. If you are flying Battleships it's very useful to be able to deploy Warrior IIs (Scout Drone Operation 5, Minmatar Drone spec 1, Drones 5). They are a great defence against small ships.
On the other hand you're not really optimised for drones so nothing wrong with just taking Drones 1, Scout Drone Operation 1 and moving on. (Bear in mind that you will probably never be optimised for drones - there just aren't enough drone skills to make it worth remapping to Mem/Per for a full year).
Phase 3: Per +10, Wil +4
Perfect 12 score for Gunnery, Missiles and most Spaceship Command skills as well as the Learning skill Clarity. 9 score for most T2 ships. This may also be a good time to take a little Focus and Presence - at least better than when you were Int/Mem.
This is the time to get good at shooting stuff, to unlock a range of your race's ships and get good at flying them. For our Amarr pvp pilot he'll want to be decent with a Frigate (4 or 5), Cruiser (4 or 5) and a Battleship. Even advanced pvpers often go out in t1 frigate or cruiser gangs. Battleship sniping is a standard role in a fleet.
More advanced ship options that you may need to master to do well in 0,0 include Heavy Assault Ships, Interdictors, Interceptors. Many corps will expect you to be able to pilot these. Ships like Electronic Attack Frigates and Logistics are likely to be more optional. You will also be expected to be able to use T1 rigs and T2 modules.
Use Evemon and plan a full year out. You may find staying Per/Wil for a long time simply because there's so much good stuff there. Possible options for a pvper are going Int/Mem and raising the level of your support skills, going Wil/Per and mastering a wide range of T2 ships or going Mem/Per and getting really good Drone skills.