I thought I'd add a bit more info in answer to the original post ("what should I save my file as?")
As others have stated, PSD, TIFF, JPEG and GIF are the formats you'll use most of the time (for print and web folks anyway).
Photoshop (PSD):
This is the format to save in by default. This gives you all the tools of Photoshop (layers, effects, type, etc.) at your disposal for continued editing. If you need to save to another format be sure to Save As (or Save for Web) so you don't lose the PSD file. Another tip-prior to saving in another format you'll often have to flatten the image, delete channels and/or paths and maybe even change the color model. Be sure not to inadvertently save your flattened file back in PSD format (or you lose all the editing ability). This is especially important if you Save for Web because once you click OK in the save box you'll be put back in your original Photoshop document (which might not be so obvious to a new user). When you close it you'll be asked if you want to save the file. If your fingers fly to fast you may accidentally write over your PSD file, very frustrating if you were doing some preliminary resizing and flattening before you Saved for Web (which strictly speaking isn't necessary to do before Save to Web but it's good to be aware nonetheless!)
PSD files are generally much bigger in file size than the other formats. Nowadays you can import PSD files into your InDesign document (Quark too? I bailed out on Quark a while ago so I'm not sure). That's nice in some respects (transparency, less work, more seamless editing), but just remember that if you PSD files are super big your file may take that much longer to image. If in doubt I'd check with the printer.
TIFF
Before the ability came to import PSD files directly into InDesign, TIFF was the popular format that you would save your images in for final print. Keep in mind that while InDesign can accept PSD files, other applications such as Word and PowerPoint don't, so you'll have to use a more traditional graphic format like TIFF or JPEG (BMPs lurk in this world too).
Unlike JPEGs, TIFFs can contain clipping paths and even transparency these days (but these features might not in turn be supported by the application you're importing into-particularly the office ones).
JPEG
You can use this for print, but it's main use is for the Web. In the print world, the thing to keep in mind is that JPEG is a Lossy format, meaning you'll lose quality as you compress the file. The compression is good when you're doing web work, but can be very noticeable in the print world. If you use JPEGs for print be sure to save them at the highest quality you can. (and we'll save the whole image resolution for another time!)
For the web, JPEG is best for photographic images. For simple color images it is usually better to use...
GIF
The other predominant web based graphic format, better for solid colors, logos, etc.
Important-if you want to save your image in either JPEG or GIF for the web, be sure to use the Save for Web function rather that just Save As. You'll get a lot more options and you'll be able to experiment with different settings to see how the image quality is affected by the reduction in file size. You can even compare how the file will look in JPEG and GIF format (sometimes it's not so obvious which one will work the best).
Well, that takes care of most of what you'll probably run into. There are some other formats that may pop up from time to time (let me tell you about DCS images for spot colors sometime!), but I'm sure I've rambled on long enough for now...!
Have fun!
Tim