Many images that you create or otherwise handle in OS X will be in the PNG format. These can be screenshots, or built-in images that are part of programs or other system resources. PNG supports an alpha channel so you can have transparent regions of an image (great for displaying on different backgrounds); however, the PNG format was intended to be a lossless format, so its inherent compression abilities are limited.
As a result, if you have a PNG with transparencies, then you might find yourself facing two possibilities for reducing its size using standard programs like Preview. The first is to change its dimensions to reduce the number of pixels in it, and the second is to save it without transparency, which is some cases may not be desired. Even if you could live without the transparencies, using a more optimized lossy format like JPEG would be the best approach.
In order to keep your PNG and its transparencies, but still reduce its size, you will have to force the use of a lossy compression algorithm. This can be done in PNGs with a program like ImageAlpha. As with any image processing that uses lossy algorithms, by using ImageAlpha you will be sacrificing image quality for the sake of file size; however, you can try several algorithms and settings in the program to find the middle ground that will work best for your image.
Note that the impact of these visual artifacts will be greater for smaller images (ie, one that is 100 x 100 pixels), and be less of an issue for large images with massive amounts of pixels that can be more easily blended using these algorithms.
By using these options in ImageAlpha, you can retain a good looking PNG file while reducing its size to about 25-30 percent of its original. Granted this is not as great as using an optimized lossy format like JPEG, but it will allow you to reduce your image size while keeping properties like transparency.
You can do the same thing online with http://optimizilla.com
There are a number of online tools that can do this; however, most will not allow you to preview the result and apply different settings levels.