Lightning has a rather small window of opportunity to complete her monumental task of saving souls before the end of the world, and she can use every bit of help she can get. Fortunately, she receives that help in spades via the Energy Point (EP) Ability system. Distribute these points properly and you'll find Lighting Returns: Final Fantasy XIII to be a heck of a lot easier.
What are EP?
EP represents a form of renewable power available to Lightning, in battle and out. EP are generated by successfully defeating enemies in battle, and the amount of points generated is typically commensurate to the difficulty level of the enemy. Minor enemies (Niblets, Gremlins) are worth a fraction of a point; stronger enemies (Anubys) may reach one EP; superior enemies (Reavers, Earth Eaters) are worth two points; bosses are worth five. EP bonuses are increased if enemies are defeated in a cloud of Chaos.
Lightning begins with a cap of five EP as a maximum. This number may be expanded to nine by completing main quests, though no higher.
EP Abilities
As Lightning progresses through her journey she will unlock a variety of EP Abilities, typically by opening treasure boxes in the Ark. All are beneficial, though some are better than others. Below is a list of available EP Abilities; note that playing on Easy Mode lowers the EP expenditure for each ability.
Used in battle, EP Abilities constitute an action that does not take away from any of Lightning's ATBs. You may use an EP Ability at any time from the EP Ability menu, assuming you have enough EP to cover the cost of the respective ability. The effects of the ability will trigger as soon as you leave the menu, making EP Abilities very handy in tight situations.
Curaga
  • Cost (Normal and Hard): 2 EP
  • Cost (Easy): 1 EP
  • Useable: In and out of battle
  • Effect: Restores Lightning to full HP.

Analysis: Curaga is a last-ditch restorative measure, though a highly effective one. It serves basically the same role as an X-Potion, fully rejuvenating Lightning's lost HP. I don't recommend using Curaga unless you're out of items (or you're in the field rather than fighting a boss and don't anticipate a great deal of trouble), but if you're backed into a corner, Curaga works just fine.
Arise
  • Cost (Normal and Hard): 0 to 3 EP
  • Cost (Easy): 0 to 2 EP
  • Useable: In battle
  • Effect: Lightning is returned to life upon fainting. The amount of HP restored depends on the amount of EP expended. If Lightning doesn't have enough EP to cover the full cost of Arise, she can only use it once; the next time she faints Arise will no longer be available.

Analysis: Arise is, like Curaga, another last-ditch, very useful ability. You want to save it until you have no other choice, as it eats up your EP like crazy. That said, even if you are out of EP, Arise will give you one last chance to get back into the fight. Phoenix Downs are preferable, so don't count on Arise in every skirmish.
Esunada
  • Cost (Normal and Hard): 1 EP
  • Cost (Easy): 1 EP
  • Useable: In battle
  • Effect: Removes all negative status effects from Lightning.

Analysis: Handy. Lightning doesn't get hit with highly-debilitating status effects all that often, but when she does Esunada can go a long way towards rebalancing the fight. I recommend saving Esunada for unfortunate instances where Lightning has been hit by two or more ailments at once; using it on one is largely overkill.
Decoy
  • Cost (Normal and Hard): 1 EP
  • Cost (Easy): 1 EP
  • Useable: In battle
  • Effect: Creates a moogle doll decoy which draws the attention of nearby enemies.

Analysis: Ehhhh. Decoy has variable usefulness. Against large mobs, which typically aren't that strong, it's pretty good. I particularly liked using Decoy against Gaunts and their annoying Aerora assaults. Against single enemies, though... eh. More often it's important to toss up timed guards and build your opponent's stagger gauge, which isn't going to happen if you've set out a Decoy.
Quake
  • Cost (Normal and Hard): 2 EP
  • Cost (Easy): 1 EP
  • Useable: In battle
  • Effect: Inflicts non-elemental damage to all enemies, raising their stagger gauges.

Analysis: Similar to Decoy, Quake is situational. It's good against crowds, but basically a waste of EP when facing larger, singular foes. It also doesn't do a ton of damage. I'm not a fan.
Overclock
  • Cost (Normal and Hard): 2 EP
  • Cost (Easy): 1 EP
  • Useable: In battle
  • Effect: Slows time for enemies while Lightning operates at full speed. Lightning's ATB gauge is considered as full throughout the Overclock effect, though stronger moves take more time away from the Overclock effect.

Analysis: Oh man. This is the number one boss killer, and the best way to take out the final form of the game's head honcho. Overclock is a staple move when the chips are down, and can help you reeeeeeally take advantage of stagger status. I highly recommend practicing Overclock until you get the hang of maximizing the damage dealt. Probably the best combat-related EP Ability in the game.
Army of One
  • Cost (Normal and Hard): 1 EP
  • Cost (Easy): 1 EP
  • Useable: In battle
  • Effect: Lightning unleashes a flurry of quick moves on the enemy while in Overclock mode. Damage dealt will restore some health to Lightning.

Analysis: Situationaly handy, though overall quite good in boss battles. Army of One allows you to add a big extra punch to your Overclock assaults, and can help pull Lightning back from the brink of death if you're running low on health. The only real downside to Army of One is that it doesn't take advantage of stagger status, so you won't get any bonus damage. Sigh. Nevertheless, this is a great ability for mashing that last bit of health away from a boss.
Escape
  • Cost (Normal and Hard): 0 EP
  • Cost (Easy): 0 EP
  • Useable: In battle
  • Effect: Lightning flees the battle. Any items or EP expended during the battle are returned. If the game's clock is active, Lightning will lose an hour of time.

Analysis: Sometimes, you've just got to run. Escape is annoying on your first play through, when you're most likely to be dying a lot, but it's still a very handy ability. (And, uh, you're sometimes given no choice in the matter.)
Chronostasis
  • Cost (Normal and Hard): 1 EP
  • Cost (Easy): 1 EP
  • Useable: Out of battle
  • Effect: Time temporarily stops, though activity in the world continues and Lightning can move freely. The effects of Chronostasis last for roughly an hour of in-game time before resuming. Events that force time forward, such as taking a train, will negate the effects of Chronostasis.

Analysis: The other must have ability besides Overclock, Chronostasis is the key to economizing on your time. Assuming you can get into battles against larger enemies with fair regularity (the Reavers in the Wildlands are a good, relativelye asy example) you can essentially stop the clock and complete quests at your leisure. In summary, USE CHRONOSTASIS.
Teleport
  • Cost (Normal and Hard): 3 EP
  • Cost (Easy): 2 EP
  • Useable: Out of battle
  • Effect: Lightning teleports to a waypoint location elsewhere in the world. These locations include North and South Stations in Luxerion; the Train Station in Yusnaan; the Train Station, Jagd Village, Aryas Village, and the Research Camp in the Wildlands; and the Train Station and Ruffian in the Dead Dunes.

Analysis: Got somewhere to be in a hurry? Teleport is pretty handy, though expensive. You'll get the most use out of it in Luxerion and the Wildlands, or if you're swapping from one region to another. It's basically useless for getting around Yusnaan, and the Cactuar statues in Dead Dunes are much more convenient than Teleport. Still, pretty awesome.