I'm familiar with some of the basics of Quartz 2D drawing, like drawing basic shapes and gradients and so on, but I'm not sure how to draw a shape with a "beveled" look, like this:
Essentially we've got a shine on one corner, and maybe some shading in the opposite corner. I think -- I didn't make this image, although I'd like to be able to approximate it.
Any ideas? This is on the iPhone, and I'd like to use built-in frameworks and avoid any external libraries if at all possible.
There are really only a few useful approaches you can take to this problem.
Use your basic shape drawing techniques and combine them with a one or more gradient curves. (Implicit object construction) with curves/fills.
Custom build a UIView and build the object up per-pixel in a drawRect.
Pre-render your beveled/shadowed shapes and load them into an image and blit them into a UIImageView.
You might want to look at the approach used by the developer here. He's still working out the implementation details, but his bevels look pretty impressive.