It's not possible to convert all of what Photoshop does to code. But much of it can be as Photoshop's features are fundamentally Core Graphics and Core Image APIs with a bit of an Adobe twist on them.
So there are three ways of thinking about this.
Mimicking what you've designed in Photoshop via Core Graphics (Quartz2D) and Core Image (kind of like filters, effects and masking tools of Photoshop) and then place everything on the screen in code. This is the hardest way, but has the smallest memory footprint and the best opportunity for performance optimisation and flexibility with animation, design and layout on the device.
Something like PaintCode, which attempts to do what I'm talking about in the above technique automagically. This is a very good app, but you have to learn many of its intricacies and paradigms, which are fundamentally rooted in what I'm talking about regarding Core Graphics and Core Image. It's not going to work with every kind of feature of .psd files, and you will have to optimise them in many ways for PaintCode to fully understand them: http://www.paintcodeapp.com
You can export all the imagery from Photoshop as various .png slices for building back together as bitmaps in Xcode, and Storyboards now has much support for doing this, plus using images in Core Animation is cry well supported. Plus this works great with the whole manner in which UIKit works. But this is the least flexible option because you'll have to not only pixel perfect place things, but you won't be able to do much without starting again on the Photoshop files. This has the largest memory footprint, potentially blowing out to dozens of megabytes (even compressed) for a universal app.
And, finally, what most people do is various combinations of the approaches above as per their requirements and capabilities.