The way I play Leona is in no way a carry or any other such thing. I play her so she has the abillity to get in and initiate a fight, repel ganks, and trying to ensure the survival of the carries. Expect to get few kills, but many assists.
Starting off with a regrowth and philo stone gives her the abillity to continually shield her carry early game. Build the philo stone as fast as possible. As usual, the boots can go either merc treads, or ninja tabi. Once you get the boots focus on assisting the carries by initiating with a combo of w q e This is a nice combo that stuns the target and allows the carries to move in. Use your ult to close gaps so your E is usable or when chasing a faster unit such a teemo or Hecarim. By the time you put your third rank in your ult, you can start using it extremely frequently. Use it to harass enemy champs or steal jungle creeps such as dragon, baron, red, and blue.