[Note: Apologies to anyone who saw the guest built one... I didn't have an account when I posted it, realized what I had just done, and don't know how to claim that one as mine.]

This Leona build is designed to counter the potential farming issues Leona can have. While it may not have what are often considered traditional choices, I explain why those aren't a big loss for the potential here to really fill the holes Leona's design comes with. The most important thing is how you start off:

First off, I take Teleport and Flash, as is described later.
Then, at the start of the round, I pick a lane (top or bottom), but do NOT go down it. I buy the Health Potion and the Cloth Armor, and WAIT FOR 40 GOLD TO TICK. Then I pick up the faerie charm, and Teleport to the front line, and you won't have missed any minion kills.

Make sure you communicate to your teammates that you are NOT AFK. They will get upset if you don't. Also, this obviously precludes early ganks. I feel that doing so is ok, because Leona is susceptible to getting hit pretty hard early on if something goes wrong.

Why do this? Well, with the Magic Resist runes + Cloth Armor, you're actually a pretty tough cookie early on. You also have the health potion to allow you to erase any mistakes by the time your teleport is back up in a few minutes. At that point, you go back and get your Philosopher's stone, and start building your Heart of Gold.

The rest of the build is explained below, and as the name of this build indicates, you'll have +14 gold per 5 for a long portion of the game, and that's great!

You're a tank. The goal is to get in there, initiate, and do two things:

Make it easier for your allies to survive.
Make it easier to kill high priority targets.

Leona can do both of these with ease. This build, as has been touched on in the intro, is designed to get you the itemization you need, rapidly, to be able to do this and rock the mid game. You'll still be effective late game, don't worry.

Laning Phase:
Harass. Use your stun at level one to just peel off people trying to gank you and your ally. If they are really dumb, you might get a level 1 kill, but don't push it. Starting at level two, you can use your sword and stun to pin someone down so you and your ally can get two or three hits in, but don't chase. You can't turret dive yet, and you don't really want to die. Remember - your teleport isn't up for a few minutes. Just be patient. Once your Eclipse is level 2 or 3, you can start packing some hurt on with the sword/stun combo. Just make sure to turn eclipse on first. You should easily be able to score a kill or two.

However, this is a gold based build. Once you have enough money for Philosopher's, find a time to go get it. Same with Heart of Gold next.

Mid Game:
You'll start roaming a bit to help with team fights as they crop up. When you initiate, I aim for whoever their carry is when I fly in, or anyone with large AOE potential (Fiddlesticks, Kassadin, and others come to mind). I use my ultimate after the initiate, because typically there is a convergence on my position, and so I get to hit more people. But the goal at this point is to keep people in the fight so your team can get kills. When you get Randuin's Omen, this becomes even easier. Just remember to use it! Don't be afraid to turret dive, just keep in mind how much it's hitting for.

Magic resist runes, because the build doesn't emphasize it, and so those few points of Magic Resistance actually go a long way towards damage reduction. The gold per 5 is because it complements the build really well.

WHY NO HEALTH RUNES??
Well, put bluntly, 100ish HP is a lot of the start of the game, admittedly, but this build packs in early resists and armor sufficient to offset that loss dramatically. Second, if you don't have a gold generating build, you will notice it. This allows you to itemize quite rapidly, and by the time you're rocking 3000+ HP, the health runes just aren't cutting it, but the resists are. (You don't need armor runes, because this build has armor covered quite well, and diminishing returns makes them a little pointless by the end).

Pretty typical 21/9 build, but emphasizing two important things:

Greed for the gold production, because you're going to want it for this build to complement all your other G/10 items and runes.

Secondly, the XP masteries. This is because if you ever leave lane to gank, or get pushed out, you don't want to fall behind in XP. A tank who is underleveled is drastically less useful.

The dodge is important, because this is one of those areas that I think this build shines. You end up with an 18% dodge chance. That's great throughout the whole game.

As has been made quite clear, it's aimed towards getting gold, and for dodging as well. However, it is also designed to keep movement of the enemy team a priority for you. Frozen mallet is better than the magic equivalent, in my opinion, because you're going to use almost all your abilities in a combo together, and so the slow from that item will be pretty much gone by the time the stun wears off, or shortly thereafter. Frozen mallet keeps it on. Also, mana isn't an issue in this build, as I've found by playing it.

Randuin's Omen helps out a lot in team fights for damage reduction and getting kills.

Guardian angel is great, because you can do your job even more with it. If you're facing a really heavy AD team, Thornmail can be considered in place of it.

Other people have a tendency to emphasize the stun ability for the sake of cooldown reduction. In the first 20 minutes of the game, I don't see Leona having as many opportunities to walk in and place a melee stun ever 8 seconds. She, however, benefits dramatically early on from having improved farming ability, so I choose emphasizing Eclipse. It also really helps with tanking, because of the huge increases in armor/resists, and the damage is actually really good chase damage, and pairs well with Flash to become a human grenade.

Teleport because the beginning of this build requires it so that you don't fall behind.
Flash because it's really useful defensively and offensively.

Make gold, itemize quickly, and hopefully just be so over-itemized compared to your opponents, that you make the mid-game period hell for them. You'll be able to turret dive, soaking up hits for a partner, with ease for extra kills, which means extra gold.

It's a fun, and different way to play Leona, and as a further bonus, the runes are really inexpensive!