Step one:
Open the image that contains the object you want to appear with a transparent background. In this case, we want the image of the sign (a stock image, courtesy of PhotoDisc) to remain and the background of the woods to become transparent.

Step two:
Use one (or more) of Photoshop's selection tools to select the object you want to remain visible. In this case, I used the Magic Wand tool to select the background. I clicked once on the forest (which selected part of the background), then I held the Shift key and kept clicking on other parts until it was all selected. Then I went under the Select menu and choose Inverse, which gives you the inverse of your selection (I had the forest selected, but I wanted the opposite, or inverse of it -- the sign).

Step three:
Convert your image into Indexed Color mode by going under the Image menu, under Mode, and choosing Indexed Color. I'm not going to explain all the options in the Indexed Color dialog box (that's a whole 'nuther tutorial unto itself), so I'm counting on you already knowing how it works. Click OK when you've put your desired optimization setting in place.

Step four:
Go under the Select menu and choose "Save Selection." When the Save Selection dialog box appears, just click OK. Then Deselect by pressing Command-D.

Step five:
Go under the File menu, under Export, and choose GIF89a Export. When the dialog box appears, under the Preview Window you'll see a pop-up menu for "Transparency From" which, by default, has you choosing a background color to be transparent. Click on the pop-up menu and instead choose Transparency From "Alpha 1". When you do this, look in the preview window. You'll notice that your background is now transparent (Adobe uses the color gray to simulate on-screen transparency, so if the background looks gray, you're there!) Now you can save your file as a GIF, the background will appear totally transparent when placed on your Web page.