You'll need to add a new target for the platform you want and will need to rebuild some view controllers since things will most likely be structured slightly differently. You'll be able to reuse the majority of the business logic, which helps.
These days with storyboards and constraints you should only need a single target. Constraints and other aspects of adaptive UI should get you most of the way there. There are only a few kinds of UI that is specific to iPads, like popovers, where your code needs two code paths. If you want to have different screen layouts for the two platforms you'll probably want to use child view controllers so the view controller code will be the same for both platforms but you'll have some parent view controllers that only are used on iPads.
Design your iPad app from scratch, what the features should be, how navigation should be, how the UI should be laid out. Ok, no see what can be re-used from the iPhone code. Does it give you ideas for changing your iPhone app? How would you do a Plus model iPhone, which behaves like an iPad when in landscape and like an iPhone when in portrait orientation.