I main SUPP and mostly i main Leona. I just wanted to show you a few builds i have made and won a lot of games with. Basic you should check who you are up against and build Armor or Magic resist. But all ways start with basic supp build : Rubby sightstone and Face of the mountain. You can in very late sell Rubby sightstone and buy more armor or magic resist.
Try different type of shoes don't stick on the basic builds all time.

Buy trinkets use them all the time. It can win you the game try to ward dragon.

For runes you can use instead of armor seals you can do Heal seals. Also you can do a combo 1 Attack damage quint instead of armor that will give you a bit of an edge early. The more armor gives you great survival skills.

These masteries i have seen in other builds and i think they are fine.

Always focus ADC or the person carrying enemy team. DONT! fight tanks and protect your adc whole game try to stick to him. Protect your adc when your team is defending. Try to sustain most of the other team attacks.

You don't need to farm just get the kills from face of the mountain so you and adc can heal.