Summary

Here is a quick list of hints:

Do everything in RGB or greyscale mode.
If the final image is to be smaller that what you are working on, wait until you have done all of the actual editing before resizing the image.
Save a high-quality version in Photoshop format before saving as GIF or JPEG. That way, if you ever need to make changes to the image you won't be starting with something which is reduced in quality.
Changing to Indexed Color mode should be the last step before saving, though it is often unnecessary because the GIF89a Export command can do this for you.
When saving as GIF:
- Use the GIF89a Export command instead of Save As.
- Try to reduce the number of colors as far as possible without making the image too dotty. Greyscale images can usually be saved with 32 colors without losing much detail.
- Avoid using the WIDTH= and HEIGHT= options of the HTML IMG tag to change the image's size. Resize it in Photoshop instead. (Thumbnails are sometimes an exception to this rule.)
- Do use the WIDTH= and HEIGHT= options to specify the actual size of the image.
When saving as JPEG, use the Save a Copy command instead of Save As.