Web graphics always need to be made as small as possible in terms of file size. A few factors that contribute to making smaller files include: reducing the color palette, using flat color whenever possible, avoiding horizontal gradients, and finally, trimming your graphics to their smallest possible size. In this case, the image to be cut out has highly feathered edges. These types of graphics are difficult to cut out by eye-balling it alone. Often times, you will end up cropping too closely and you will see a hard edge once the image is on the Web (as shown).
1. Merging layers
If the image is in multiple layers, merge them together. Use the Option Merge technique to keep the source layers intact.

TIP: Instead of using option + merge, you can simply turn on all the eyeball icons of the layers to be merged, and select Duplicate from the Image menu. Check the Merged Layers Only check box to create a new merged file apart from your source file.

2. Using the magic wand to find the edges
Using the Magic Wand tool, set on a tolerance of zero and with no antialiasing, select the transparent background surrounding the image. To ensure that you capture all the transparency, choose Similar from the Select menu. Invert the selection. This selection shows you the absolute outer edges of your image.

3. Creating a rectangular selection
In order to crop the image according to the selection created in Step 2, you need to convert the selection into a rectangular one. Hold down the shift key to add to the current selection using the Marquee tool until you have a perfect rectangle. Because you are adding to the selection, you do not have to do it all in one step; you can build it in stages. For example, start at the top-most point and draw to one of the side-most points. If the Crop function is grayed out in the Image menu, your selection is not a perfect, there may be a tiny bulge somewhere. Crop the image with the Crop function once the selection is perfect.