Get a Tear of Goddess. That will solve most of your mana issue. Upgrade it later, after you get your core items for a nice amount of AP.
As Sona, all you need to do is maintain your life and your position. Most of the time when Sona died, the whole team will fall apart, and the enemy knows that, so try to live as long as possible. Prolonging battle is one of Sona's advantage, and that's why I never like poking game against her. Don't forget that "Sona stance", where 3 of your fingers are on QWE and just mashing them
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I won 90% time I use Sona, so I feel like dropping her already. I like her appearance, and her skillset, but for some reason it doesn't feel good using her.