Please understand this is part of a long-term plan! Don't be discouraged that you need all these skills at all these levels in order to get into PVP. You don't. These are just to give you an idea of what you need to work on over time.
With thanks to Cal Nereus.
These are all the skills you need to fit all your desired modules onto your ship without running out of powergrid or CPU.
Engineering: 5% Bonus to ship's powergrid output per skill level.
Electronics: 5% Bonus to ship CPU output per skill level.
Energy Grid Upgrades: to fit Power Diagnostic Systems, which increase powergrid.
Electronics Upgrades: 5% reduction of sensor upgrade CPU needs per skill level, and to fit Co-Processors.
Shield Upgrades: 5% reduction in shield upgrade powergrid needs.
Weapon Upgrades: 5% reduction per skill level in the CPU needs of weapon turrets and launchers.
Advanced Weapon Upgrades: 2% reduction in powergrid needs of weapon turrets and launchers.
I believe the most common benchmark for PvP Fitting Skills is to have Engineering, Electronics and Weapon Upgrades all up to level 5, and Advanced Weapon Upgrades up to 3. The others can be at the level of your choice.
Basic Capacitor Skills
These are all the skills you need to optimize the size, recharge rate and efficiency of your capacitor. As many Eve players will attest to, cap is life in Eve. If you don't have it, you're dead.
Energy Management: 5% bonus to capacitor capacity per skill level.
Energy Systems Operation: 5% reduction in capacitor recharge time per skill level, and to fit Capacitor Boosters.
Energy Grid Upgrades: to fit Cap Rechargers (I already mentioned this skill as a fitting skill earlier).
Energy Emission Systems: 5% reduced capacitor need of energy emission weapons per skill level, and to fit Nosferatu.
You'll want Energy Systems Operation at level 5 and Energy Management to level 4 at least. Cap Rechargers or Cap Boosters are prevalent in most PvP fittings, so you'll want to be able to fit the best.
Anyone planning on using frigates or microwarpdrives in PvP (in other words, just about everyone) will need to consider training most of the Navigation skills.
Navigation: 5% bonus to sub-warp ship velocity per skill level.
Acceleration Control: 5% Bonus to Afterburner and MicroWarpdrive speed boost per skill level.
High Speed Maneuvering: 5% reduction in MicroWarpdrive capacitor usage per skill level.
Evasive Maneuvering: 5% improved ship agility for all ships per skill level.
Frigate specialists need to seriously consider training all of these skills to level 5. Personally, I'm a Battleship pilot, and even I have Navigation trained up to 5. If you plan on piloting Interceptors or Interdictors, you will need Evasive Maneuvering up to level 5 just to sit in your ship.
Almost all PvPers (actually, pretty much all of them) need to train up their tackling skills. These are the skills you need to prevent your target from escaping.
Propulsion Jamming: 5% Reduction to warp scrambler and stasis web capacitor need per skill level, and to fit warp scramblers/disruptors and stasis webifiers.
Energy Emission Systems: To fit energy neutralizers to kill the target's cap (this skill was also mentioned earlier as a basic capacitor skill).
Anchoring: Used to deploy and anchor various items, including mobile warp disruptors.
All PvPers will want to train Propulsion Jamming, preferably up to level 4 at least. Specialists in the field of tackling will want it trained to level 5. Anchoring is largely optional, but in 0.0 I've seen it used a lot to anchor bubbles.
Armor Tanking Skills
Armor tanking is without a doubt the most common form of tanking in PvP, which is great for the Gallente and Minmatar races, but makes things difficult for the Caldari ships. Amarr prefer armor tanking their own ships, but hate when their enemies do it.
Mechanic: to fit Armor Repairers.
Hull Upgrades: Grants a 5% bonus to armor hit points per skill level, and to fit Active Armor Hardeners and Plates.
Repair Systems: 5% reduction in repair systems duration per skill level, and to fit Armor Repairers.
EM Armor Compensation, Explosive Armor Compensation, Kinetic Armor Compensation, Thermic Armor Compensation: To improve passive/inactive armor resists.
Most PvPers seem to believe Mechanic and Hull Upgrades should be trained up to level 5, and Repair Systems up to level 4 to fit all the modules you will need. The compensation skills should also be trained up to level 4, or at least 3 if you don't have the patience for 4.
Electronic Warfare Skills
Electronic Warfare is a major part of fleet PvP, and useful in gang PvP. With the right combination of E-War you can practically turn off an opponent's ship. Combined tackling and E-Warfare can render even the sturdiest tank and most ominous firepower absolutely useless.
Electronic Warfare: 5% less capacitor need for ECM and ECM burst systems per skill level.
Sensor Linking: 5% less capacitor need for sensor link per skill level, and to fit sensor dampeners.
Long Distance Jamming: 10% bonus to optimal range of ECM, Remote Sensor Dampers, Tracking Disruptors and Target Painters per skill level.
Signal Dispersion: 5% bonus to strength of all ECM jammers per skill level.
Frequency Modulation: 10% bonus to falloff for ECM, Remote Sensor Dampeners, Tracking Disruptors and Target Painters per skill level.
Train Electronic Warfare to level 4 at least, but it's up to you how far you want to take all of the other skills. The aforementioned skills only touch upon the most common forms of E-Warfare: ECM and Dampening, and I believe it's possible to specialize much further in this category of PvP.
Up until now I haven't even mentioned the relevant gunnery, missile and drone skills you need for PvP to actually deal damage to your target(s). To be honest, there are simply way too many such skills to mention, and the ones you use are entirely up to you. Most PvPers prefer guns, specially hybrid turrets and projectile turrets. Some skills that can apply to all guns are Motion Prediction, Rapid Firing, Sharpshooter, Surgical Strike and Trajectory Analysis. Seriously consider training each of those to level 4 or 5.
All of this information is from 2007, and while I think it's all still relevant today, if anyone can show anything here is incorrect, please leave a comment and I'll update it.
Good luck with your PVP!