Think carefully about what you want to photograph. Think about the different angles you can take the photograph. Think about using/not using props, as well as your background. Some of the most beautiful images I have seen have plain, white backgrounds that don't distract.
Then snap, snap snap. Take 2 photo's of the same thing, heavens go ahead and take 100! Each time try change one thing and then look at which ones you like the best.
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Natural light works wonders! Try placing objects near a window for soft, natural looking images. Bright natural light when enhanced with Instagram effects, for example Valencia, will give you a similar look and feel to these two images below.
I mainly use the wonderful A Beautiful Mess app when editing for Instagram. It's one of my favourite apps for adding text, frames and cute doodles onto photographs. A lot of the images in my Instagram feed have been edited in the A Beautiful Mess app, and then uploaded to Instagram and run through different effects until I am happy
A Beautiful Mess app can be found on the Itunes store (click here). The app itself costs $.99 and is packed full of features. You can purchase additional effects/doodles/borders/text easily through the app itself. I have the basic $.99 version and its perfect for what I need.