Only gifs and pngs can add an alpha (transparency) channel and be used on the web. For print, an eps file is usually used, but for your purposes I'd go with the former.
In Photoshop, grab everything you want to show and place on a new layer (or "select inverse" and delete), then delete everything from the first layer making it transparent. Separating an object from it's background is called silhouetting and there are a few ways to do it. The best is to trace a path around the object, then select the path which will marquis what you traced. It takes a bit of practice.
Then, from the file menu, select "Save for web and devices", then save as a 24 bit png. The "ping" file will be larger than a gif, but look nicer, especially if there are a lot of colors, gradients, etc. If black and white, try a gif. Or both and see what you like vs file size, if that's an issue.
By the way, best rule of thumb, the image should be the exact size you want or larger and 72 pixels for screen (266 pixels for print).
If your final image has too sharp and edge, or if you see white or black artifacts, there are tools to help. Under "layers", bottom of the pulldown play with the matting for removing artifacts and defringing and under "select" check out the "modify" section. Feathering is a great technique to learn, but not here. You can probably find some tutorials on youtube.
Lastly, the poormans way of achieving the same effect as transparency is to make your image's background color the same as the background where you intend to place it. Doesn't work with gradients or on top of another image, but fine for plopping it on top of that ugly military green.
Save it as a jpg or bmp or anything you prefer.
That help?
Dave
Resolve then, that on this very ground, with small flags waving and tinny blasts on tiny trumpets, we shall meet the enemy, and not only may he be ours, he may be us. --Walt Kelly