Sometimes when you make an image you see that it doesn't like "right", so to say, with the background of the webpage you are viewing it at, which is where a border is very handy.
Making a simple border around a complete image without cuts is simple. Make a new layer and hit Control-A (or Select>all) and go to Edit->Stroke, and fill it in. When using this dialogue box always remember: to choose an approriate size border, to choose a border that blends with your image and doesn't contrast too much.
Now for cut images and adding borders. You want to again make a new layer. This time you want to select everything that isn't a cut. You can do this in many ways, here are two.
One: Merge all the layers (Layers: merge visible) then using the Magic wand Tool click on the transparent areas of the layer you have there. Then hit Control-Shit-I (or Select-Inverse) and then Edit stroke.
Two: Select the layer transparency for each layer (on the layers palette hold control and click the layer Thumbnail) then to select more than one layer transparency hold Control and Shift and click the thumbnails of each layer, then use Edit stroke again.
I prefer method 2, since you don't sacrafice the layers being merged. I apologize for the lack of images in this tutorial.