The simplest way to do this, if all you want is pinch zooming, is to place your image inside a UIWebView (write small amount of html wrapper code, reference your image, and you're basically done). The more complcated way to do this is to use touchesBegan, touchesMoved, and touchesEnded to keep track of the user's fingers, and adjust your view's transform property appropriately.
Keep in mind that you're NEVER zooming in on a UIImage. EVER.
Instead, you're zooming in and out on the view that displays the UIImage.
In this particular case, you chould choose to create a custom UIView with custom drawing to display the image, a UIImageView which displays the image for you, or a UIWebView which will need some additional HTML to back it up.
In all cases, you'll need to implement touchesBegan, touchesMoved, and the like to determine what the user is trying to do (zoom, pan, etc.).
Another easy way to do this is to place your UIImageView within a UIScrollView. As I describe here, you need to set the scroll view's contentSize to be the same as your UIImageView's size. Set your controller instance to be the delegate of the scroll view and implement the viewForZoomingInScrollView: and scrollViewDidEndZooming:withView:atScale: methods to allow for pinch-zooming and image panning. This is effectively what Ben's solution does, only in a slightly more lightweight manner, as you don't have the overhead of a full web view.
One issue you may run into is that the scaling within the scroll view comes in the form of transforms applied to the image. This may lead to blurriness at high zoom factors. For something that can be redrawn, you can follow my suggestions here to provide a crisper display after the pinch gesture is finished. hniels' solution could be used at that point to rescale your image.
(Shefali's solution had the downside that it did not scale continuously while pinching. Furthermore, when starting a new pinch, the current image scale was reset.)