To make a circular button, you can just use the corner radius property! So long as the frame/bounds of the button are a square, if you set the cornerRadius to half of the width, it'll appear as a circle. First, you'll need to import the QuartzCore framework:
import QuartzCore
Corner Radius
To set the corner radius:
myButton.layer.cornerRadius = 8.0
To make a circle given an arbitrary frame, you can use the following:
myButton.layer.cornerRadius = myButton.frame.size.width / 2.0
You may have to set the clipsToBounds property for the corner radius change to be visible:
myButton.clipsToBounds = true
Border
You can also use the layer property to set your border:
myButton.layer.borderWidth = 1.0
myButton.layer.borderColor = UIColor.purpleColor()
(See this post for more examples in Objective-C)