There exist many different formats you can use to save your pictures - but which are the best? That depends on their use. Here are some common formats:
If you're going to save pictures you want to use on the net, use Save for Web in Photoshop. it gives you an interactive way to compare file size vs. quality, plus it doesn't save unneccessary extra information this way.
1. When I save my pictures, the quality degenerates each time.
This happens when you save your pictures as JPEG (or other formats which loses quality during compresion.) Each time you save a picture in the JPEG format, it is compressed, and you lose more and more details and colour information.
2. My digital camera saves the pictures as JPEG. How should I treat the files when I'm editing them?
Save your files as PSD or TIFF, depending on wether you want to continue editing or they're finished. Save only as JPEG when they're finished and shall be published (in addition to a TIFF file with full quality - in case you'd like to edit further or use it on a later stage.