To animate along a smooth curve, you'll want to use a CAKeyframeAnimation. In this answer I provide code for a combined animation that moves an image view along a curve, while resizing it and fading it out. The relevant part of that code is as follows:
// Set up path movement
CAKeyframeAnimation *pathAnimation = [CAKeyframeAnimation animationWithKeyPath:@"position"];
pathAnimation.calculationMode = kCAAnimationPaced;
pathAnimation.fillMode = kCAFillModeForwards;
pathAnimation.removedOnCompletion = NO;
CGPoint endPoint = CGPointMake(480.0f - 30.0f, 40.0f);
CGMutablePathRef curvedPath = CGPathCreateMutable();
CGPathMoveToPoint(curvedPath, NULL, viewOrigin.x, viewOrigin.y);
CGPathAddCurveToPoint(curvedPath, NULL, endPoint.x, viewOrigin.y, endPoint.x, viewOrigin.y, endPoint.x, endPoint.y);
pathAnimation.path = curvedPath;
CGPathRelease(curvedPath);
This creates a curve with two control points, one at the origin of the view and the other at the upper-right corner of the the display (in landscape mode). For more on constructing paths, see the Quartz 2D Programming Guide or the Animation Types and Timing Programming Guide.
To use this animation, you'll need to add it to your view's layer using something like the following:
[imageViewForAnimation.layer addAnimation:pathAnimation forKey:@"curveAnimation"];
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