Shield of Daybreak

Shield of Daybreak is a 1 second stun. You should use it after you engage with Zenith Blade. Shield of Daybreak empowers your next auto attack meaning that you can use this to reset your AA. This can be used on towers or wards (AA->Q->AA) for extra damage

Eclipse

Eclipse is a boost in defenses and Leona's main damage source. It should be used before engaging with Zenith Blade so that it will reactivate before the enemy has time to dodge.

Zenith Blade

Zenith Blade is a 0.5 second root and Leona's gap closer. This is the main ability which makes Leona who she is as a champion. Zenith Blade is the ability that you will use to engage.

Solar Flare

Solar Flare is an AoE stun in the middle and a slow on the outer edges of the circle. As this ability has a slow cast time, you will often need to use it after Shield of Daybreak or Zenith Blade or a teammates CC to make sure that you can land the stun.

The ability levelling is pretty standard in each game; Solar Flare-> Eclipse-> Shield of Daybreak-> Zenith Blade.

The most useful order in which to use your abilities in Eclipse then Zenith Blade then Shield of Daybreak then Solar Flare (If you have it).
This allows you to get the most damage and CC possible. Weaving in an AA after Zenith Blade will also add extra damage then resetting the AA with Shield of Daybreak.
It is unadvisable to use Solar Flare without any prior CC as it is a easy to see and slow moving spell meaning that enemies will have plenty of time to react.

Aftershock is the most optimal rune for Leona. It gives tankiness, is easily activated and the damage is easy to land due to Leona's CC.
Font of Life is a great rune for the same reason as Aftershock. It is easy to activate with multiple CC and the heal synergises well with the health stacking on Leona.
Bone Plating is great for the short trades Leona is in however, against mages such as Zyra or Brand, Second Wind is the better option in order to survive laning phase.
Overgrowth is the best option of this tree as the the health is needed due to items such as Locket of the Iron Solari not giving health or very little.
Biscuit Delivery is the best rune choice as the Biscuits give Leona that extra sustain in lane.
The 5% CDR gained from Cosmic Insight is extremely useful as Leona uses all of the CDR provided by this rune. This CDR in conjunction with the CDR provided by the stat shards gives Leona more opportunities to fight more and win lane more easily.

Cooldown Reduction gives extra early game pressure.
Armour/Magic Resist can be switched out depending on the matchup, however, Armour is the stat shards you will take most as it helps when engaging using Zenith Blade.
Health is a great defensive option however, against full AD/AP take Armour/Magic Resist.

Relic Shield is the best support item to start as the health, execute and healing makes for an easy laning phase. One thing to note is that you should only take either one melee minion or siege minion from a wave. Using the Relic Shield execute on a caster minion gives less gold.
Mobility Boots are the best option as they allow for quick and easy roams mid lane or to help the jungler. However, if your ADC needs peeling and your team has enough engage, Mercury's Treads can also be bought to add extra tankiness. This be purchased if the enemy team has a lot of CC as well.

For the following items, they are in no particular order of when to buy them.
Knight's Vow is a great support item in general and excellent on Leona. The healing received from this item is extremely useful when diving the enemy the team and the damage redirection is helpful for the survivability of your own ADC.
Locket of the Iron Solari is a nice item to have if the enemy team has a lot of AoE. The health accumulated via runes and items synergises well.
Zeke's Convergence is another great option as Leona's ult,being a stun, makes it easy for your ADC to walk up and land their AAs igniting the frost storm.
Redemption is good for a siege comp as the extra healing allows for a longer siege. The mana regen and health regen also gives Leona more opportunities to go in without worrying about resources.
Turbo Chemtank is a great item for when you are extremely ahead or the enemy teams has a lot of mobility. The movement speed gained can be combined with Shield of Daybreak then Zenith Blade for an easy kill.
Gargoyle Stoneplate is one of the best items on Leona. It gives a large amount of defenses and the health gained through it is extremely useful. When activated after engaging with Zenith Blade it gives makes Leona almost unkillable.

The easiest way to engage as Leona is to use Zenith Blade on the enemy backline then following up with a Shield of Daybreak on the most fed/easiest to kill target (usually the enemy MID/ADC) and using Solar Flare to stun/slow as many targets as possible.
However, before you engage/start a fight, you need to make sure that you will win. Also be sure that your team is in a position to engage e.g. in lane, don't go in when your ADC is about to take a cannon minion or is too far away from the enemy minion wave.

Engaging is not the only thing that Leona can do in teamfights. Leona's CC is also a great way to peel for your carries. If your team already has enough engage then your main priority is to make sure that the damage dealers on your team won't get easily killed.