I have played maaany times Sona, I actually main her, and I have tried lots of builds. I found out that playing AP is the best way to actually help your team and yourself.

So, at early game your goal is to earn gold (and keep an eye to your adc of course). Just spam your Q at enemies, that way you get gold and you give them a hard time. Also use your trinket when you have it, I see many AP supps who don't use it at all and you get a gank from nowhere. If you get ganked use your W as it gives a shield to your allies and E to run away. If you have your ult use it on jungler, is the best way to ensure your escape. Try not to take kills, just deal enough damage so your adc can finish them. If you are gonna main AP supp you may find it difficult at first not to take kills, but as you get used to it you will be the best :) Also try to be safe from CCs.
At mid-end game (when lanes actually are a mess) try to keep your ult for help at teamfights. An AOE stun is always useful ;P OFC you can always use it to take 1v1 kills cause its fun, but try to focus on helping, or the team will have no support. Unless you see your team is good and does not actually need a supp (that's rare though).
Sona deals damage mostly with her Q and her passive. When your R is ready its fine, BUT if it's on cooldown you must careful cause 1 Q and passive will not always give you a kill and when your Q is on cooldown you have nothing. So if an enemy hunts you down and think you can beat him, use your Q+passive then retreat using W+E (just so you get again your passive) then turn around to Q+passive him again and do that all over until you are safe.
When in a teamgifht focus your damage and your stun on the most fed enemy. The stun will make him useless and your damage is vital to end him. Don't forget to use your heal too, AOE healing and shielding is op. Try to keep your distance from champions that counters Sona cause she died really fast and she is very helpful for the team. Sona is actually one of the few supps you must focus at an enemy team.
Playing against her : If you have very ranged skills like Lux, don't go close to her, spam her from distance, she must come closer to deal damage on you. When Sona's passive is ready, there is a circle around her. This circle is: blue if the empowered hit will have Q's effect, green for W's effect and purple for E's effect. Especially when the circle is BLUE keep away. A good Sona player can beat most of adcs but if you have enough damage and you hit her first you can end her. Also she is good against champions with no CCs so if you have CC or stun or something like that use it on her. If your CCs are on cooldown wait for them. Most important, do not underestimate her, many do that and give kills to her. Especially under enemy turret you are a free kill. It's not worth to give her kill even if you kill her, she mustn't take items.

Pros:
High damage
Q has low mana cost
Has AOE stun/heal/speed
Good teamfighter
High mobility

Cons
Average cooldowns
Vulnerable without R
W+E have high mana cost
Vulnerable at CCs
Not very efficient at 1v1 without R

I know this may be a strange build for a supp, but her damage is a really good help for the team and without it she can't even solo minions :P I hope you found this guide helpful and that you will enjoy my build if you try it :)