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Built like a tank with some damage..nothing more to say.

Pros:

First Female Tank
Lots of CC (2 Stuns,1 Suppress)
Great Peeler
Can completely shutdown champions

Cons:

Partner Dependant (Needs someone that will harass when you harass/skill spammy champions)
Low AP ratios/Lack of OP Damage (About the same as Morde)
Semi-Squishy Early Game

Teleport: She's rather slow so those trips back don't take forever.

Exhaust: For the obvious defensive/offensive reasons

Shutting down a carry's damage
Slowing a person and reducing their armor/resistances for more damage.

Tip: Exhaust one carry and completely stun lock the other and the opposing team has no damage at all in teamfights.

Other useful spells:
Flash, because she really doesn't have any escape abilities.

Ghost, same reason as flash but longer escapes they can be used in different situations.

Ignite, for champions that heal a lot like Gangplank/Vladimir/Xin Zhao and just added damage to your bursting combo.

Fortify, make sure and drop a point in the Harden Skin mastery and get Improved Fortify for the amazing splash damage and saving turrets/stunning under turrets.

Early game: Q+W (Stun+AoE)

Farming: Weaken E then W (Keep in mind you want to save your mana and not push lanes but for those times when it doesn't matter this combo deals sufficient damage.)

Initiation w/o Ult: W>E>Q>Exhaust

Initiation with Ult: R>W>E>Q>Exhaust (Start with your ult for your passive to hit everyone in the teamfight so your teammates will do more overall damage.)

Sunlight(Passive):
Leona's damaging spells affect the target with Sunlight for 3.5 seconds. When allied champions deal damage to those targets they consume the Sunlight debuff to deal 20 / 35 / 50 / 65 / 80 / 95 / 110 / 125 / 140 additional magic damage. Leona is unable to activate the additional damage herself.

This is the reason why you shouldn't solo lane/mid/jungle on Leona. Also, it means that you need to constantly be harassing and be ontop of making sure that you initiate fights so the rest of your team can do extra damage.

Tip: Great addition to dps skill champions like MF's Ult/Akali/(Insert Skill Spammy Champion Here)

Shield of Daybreak(Stun):
Leona's next basic attack will deal additional magic damage and stun the target for 1.25 seconds
Cost: 45 / 50 / 55 / 60 / 65 mana
Cooldown: 12 / 11 / 10 / 9 / 8 seconds
Magic Damage: 40 / 70 / 100 / 130 / 160 (+0.3 per ability power)

This is your short stun that you should use for harassing/peeling. As you can see the stun does NOT scale to become longer with more ranks; therefore, it's a great idea to max this last after getting the first point.

Eclipse(AoE/Farming/Shield Ability):
Leona raises her shield to gain bonus Armor and Magic Resistance for 3 seconds. When the effect ends she deals magic damage to nearby enemies and prolongs the effect for a bonus 3 seconds if any enemies are struck.
Cost: 60 mana
Cooldown: 14 seconds
Armor & Magic Resist Bonus: 30 / 40 / 50 / 60 / 70
Magic Damage: 60 / 110 / 160 / 210 / 260 (+0.4 per ability power)

Reason for maxing this first is because the cost doesn't get any more expensive and it has the highest damage output out of your 3 normal skills. Unfortunately, you can't blow this up when you want to so you have to be perfect on the timing of this skill to land it and get the additional 3 seconds of added Armor/MR. This is your harassing ability. When you think of the damaging factor of this skill it's kind of like Sion's Shield when it blows up. So, you can do a Sion combo(Stun+Shield Explosion) during laning phase.

Tips: Stun+Shield combo only costs 105 Mana until level 14. Really cheap for a lot of steady damage.

Zenith Blade(The initiation skill):
Leona projects a solar image of her sword, which deals magic damage to all enemies in a line. When the image fades, the last enemy champion struck will be briefly immobilized and Leona will dash to them.
Range: 700
Cost: 60 / 65 / 70 / 75 / 80 mana
Cooldown: 13 / 12 / 11 / 10 / 9 seconds
Magic Damage: 60 / 100 / 140 / 180 / 220 (+0.4 per ability power)

The damage output is higher than the stun, so you max this next. Nothing extremely special about this skill besides the .5 second suppress.

Tip: Using Eclipse right before you use this = lots of damage and then add your 2 stuns. You can completely lock down one champion just with this combo.


Solar Eclipse(Great Initiator+Stun+AoE damage):
After a brief delay, Leona calls down a beam of solar energy dealing damage and slowing enemies by 80% for 1.5 seconds. Enemies in the center of the beam are stunned instead of slowed.
Range to Center of AoE: 1200
Cost: 100 / 150 / 200 mana
Cooldown: 105 / 90 / 75 seconds
Magic Damage: 150 / 250 / 350 (+0.8 per ability power)

Reminds me of Amumu's ult but the stun/slow is shorter and it also has less scalability and isn't a for sure stun and has a delay. So, why is this better than Amumu's ult? The cooldown is much shorter, and by much I mean it's half the cooldown. Meaning, you don't need to worry about the skill being on cooldown for every team fight. Attempt to use this everytime it is up.

9/21/0

The 9 in Offense is a pretty standard build for any AP champion.

Enhanced Exhaust for the easy First Blood.
Cooldown Reduction/Magic Pen always helps.

I take 21 in Defense because you are the tank.

You get Early HP/AP/Survivability in general.

Flat HP Quints (Early Survivability)
Magic Pen Reds (More AP Damage)
HP/Lvl Yellows (More Late Game HP since you're not getting any HP Items besides Omen)
Flat MR Blues (More MR never hurt)

Optional:
Quints: Movementspeed (For easier stunning)
Reds: Armor/MR/HP (More Survivability)
Yellows: Armor/Dodge[With Dodge Masteries] (More Survivability to counter AD Champions) or MP5/MP5 per lvl (If you find yourself going Out of mana early/late game)
Blues: CD Reduction (More stuns) or MP5/MP5 per lvl (See above reason)

Reason I get some AP items in the beginning is to make the opposing team think/know you're a threat and once that has been accomplished. They will start to target you and at this point you have done your job as the tank.

Start with:
Regrowth Pendant + HP Pot (sustainability)
Boots + 3 HP Pots (easier last hits/stuns)

2nd Trip:
Boots + Ruby Crystal + Amplifying Tome

3rd Trip:
Finish the Sorc Boots/Merc Treads (If you're going against a heavy CC team if not you don't need the extra MR) and Haunting Guise

4th Trip:
Finish the Force of Nature (Now you should have some decent movement speed and extreme MR..even a fed Lux won't make you budge.)

Tip: You don't need health pots once you finish the FoN. From this point on, always buy at least 1 ward every trip back.

5th Trip: Warden's Mail + possible Heart of Gold (The passive on Warden's Mail is extremely beneficial)

6th Trip: Finish Omen's Randuin + Negatron Cloak/Chain Vest (Doesn't depend on the team..it depends on who is doing all the damage and who needs to be shutdown. Your next item should be focused towards that person. Whether it is an Abyssal Scepter/Zhonya's Hourglass both are what I call AP/Tank Items because they have decent AP/Major survivability.)

7th Trip: Finish Abyssal Scepter/Zhonya's Hourglass and start on the other.

Tip: Buy Red/Blue Elixirs from here on out.

8th Trip: Finish the other item and now you can sell the Haunting Guise for either a Rabadon's Deathcap or Warmogs because you have enough Armor/Magic Resist at this point

You should be unkillable at this point and have a decent amount of AP (200+), so you're not only a tank that can stun but a decent threat as well.