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.
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.