This is a very common question I get from friends on my Instagram, and the first thing to understand is what type of photos the iPhone is capable of taking.
1. Landscapes in good lighting
2. Food photos
3. Generic people shots
4. Street photography
This is by no means a complete list, but it is just the things that are coming to mind as I write this.
Step two is to download a decent photography app, I personally use Adobe Lightroom as it allows me to shoot in RAW format. What this means is that it allows the camera to capture a lot more detail that you can adjust in post processing without damaging the quality of the photo. It does take a lot more space on your phone, it is slower than the basic camera app but the results are definitely worth the trouble in my opinion.
Step three is to take time to compose your shot. Think about what you are trying to convey with this photo.
What is the main focus or subject?
How does it relate to the background?
Are there objects in the background that can be avoided to provide a cleaner image?
Is the photo level horizontally?
This is perhaps the most difficult part as it takes a certain amount of practice to be able to compose photos first in your mind then translating that onto your phone screen.
There are many other guidelines that you can follow, such as the golden ratio or the ratio of thirds. This is a whole separate posts and I could go on forever based on the different types of situations. Note* if you wish to shoot in RAW format in the Lightroom APP you must shoot with the APP and make sure that the DNG is selected not JPEG. (DNG is Adobe's extension for RAW)
Step four is the post processing of the photo.
Once you have taken your shot in Lightroom APP, select your photo and play around with each of the options. It is reasonably self explanatory what each slider is for, they are clearly labeled Exposure, Contrast, Highlights, Shadows etc.
How you process your photos and the style in which you prefer differs and there is no right or wrong when it comes to aesthetics.
Here are a few examples I took with my iPhone 6s:
What I have basically done to process these photos include:
1. Increasing the contrast
2. Increasing the Vibrance
3. Increase a bit of the shadows
4. Reduce some highlights
5. Slightly increase the saturation of the colors
6. Some cropping and straightening of the photos to make sure it is level
So there it is, I hope you find these tips useful!