First thing's first, why use Leona? I have used several tanks before, and to me, most of them have no reason to get focused in 3v3's and get ignored the whole time. Leona has two types of CC (her ult has a fairly low cooldown as the game goes on) and she does some decent damage early on with her W. This is why I've found her to be effective on 3v3's, if you dive into the middle of the enemy, you have a decent survivability factor, and if they ignore you, there are between 2 to 3 stuns you can pull off that change the tide of the fight very quickly.

All of Leona's Runes are about lasting longer earlier. Marks of armor for taking that extra hit early on, slightly negating some of the more early damaging champs like Tryndamere. The Seals are dodge runes because again, avoiding a hit can make the difference between living and dying, especially with champions with on hit effects (Jax). The Glyphs are magic resist for surviving early bursting champions, and are about staying in the lane as long as possible against champions such as Brand, who are effective at sending you back. The Quintessences are straight health, for the same reasons stated above. Living in your lane can make all the difference between getting early kills for your partner, or getting killed early on.

As stated with the runes, these are fairly straightforward. They negate several points of damage early on, both from creeps and heroes, as well as giving extra health. All of these are pivotal in surviving and winning early encounters with your partners.

I know the first thing everyone's thinking is "really... heal?" The only thing I can answer to that is one of your biggest jobs as Leona is to keep the squishier members of your team alive, and heal is a good way to do that. A heal in addition to a W-Q when running away with a team-mate who is almost dead can mean the difference between survival and a 30-second absence in mid-game. Exhaust does the job well too (Slowing and reducing damage aren't to be overlooked) but having used both repeatedly, I find that little bit of extra health can often negate the one dive skill the opponent uses while giving you time to rope them in and stun them. Flash is there because it is simply a great spell, both offensively and defensively.

I use this skill order because of the double effect Leona's W has. She gets a nice early boost of a ton of armor, and on top of that, from levels 7-15, the damage done by her W can't really be ignored, and it extends further if there are squishies on the opposing team. The skill order that can really devastate any opposition that isn't a tank is W (wait one second to let it warm up) then a quick Q into an immediate E. It starts your explosion and jumps you to them while stunning them. When done in combination with an astute laning partner, this is essentially a free kill in the mid game, or bare minimum will make them retreat and heal, giving you control of the lane.

As I'm sure anyone reading this has noticed, her items are a bit tank scattershot early on. They provide health, armor, and magic reduction, all of which improve your ability to keep your teammates alive (and lets you dive into fights much easier regardless of who you're facing). Obviously, you need to be flexible based on your opponents. Examples are, if your team is rolling the enemy early, take advantage and skip the Warden's Mail and the Negatron Cloak and go straight into finishing your Trinity Force, or if there's a strong/fed mage on the other team, go for magic resist early. That's one of the reasons for the variability of the build, it's very neutral until the game can dictate what you want to go for.

Pros

Leona is very tanky. Will survive through many things that seem like definite deaths.
Fun to play, with a skill set that lends itself to bursting.
Extremely effective when paired with a damage dealing partner, particularly carries or squishier mages.
2 types of CC effective at initiating team fights.

Cons

Not much damage output.
Only useful if the team has other damage dealers.
Long Cooldowns (occasionally missing out on kills/assists because of it)

Leona's farming is certainly interesting, because for the most part, you only want to when your partner isn't there. For the most part, you are there entirely to set up your partner for kills and creep kills. Later on, W tends to take out most hordes of creeps very effectively and is a good way of clearing out lanes later on.

Don't. This build is not for jungling, and even at level 18, almost fully built, it can take over 15 seconds to get red buff. Most of your ability is based on your CC, so jungling would be a waste of a summoner spell, and your usefulness in instigating and prolonging teamfights.

This is my first guide, and I just wanted to share because I've had a pretty good amount of success with it while playing 3v3's. I welcome any constructive criticism or feedback that anyone has, and will hopefully be updating this based on responses or solid ideas. This is by no means a pro guide and shouldn't be treated as such, but as I said, I've experienced quite a bit of success with it, and hope you can too. Good luck Summoners!