This tutorial covers only the very basic settings of the Image Optimizer.
The Save As function under File should only be used when saving/converting a file to a different format and/or renaming the file; for example, saving a jpg as a gif, png, et cetera, or changing project1.jpg to project1b.jpg.
You can make a duplicate of your opened UFO (CTRL+D) and work with it instead of your original (a good idea, I think, if you find PI freezes up on you).
SAVING AS A GIF
1. To save selected objects:  With your Pick Tool (Fig. 1), left click on each piece you want to save to activate them. You will see a dotted line ("marching ants") around the selected/active objects (Fig. 2). Proceed to Saving an Image. (*See below to learn how to select all objects.)
    To save entire image:  Make sure you have no active objects and skip to Saving an Image.
                                                                Fig. 1                       Fig. 2
     

2. *To merge all objects:  With one object activated, Right click/Select All Objects and then Right click/Merge as Single Object. Proceed to Saving an Image.   Note:   This does not save your background.
   

SAVING AS A JPG
Make sure you have no active objects and skip to SAVING AN IMAGE. (This will save your background too). Too easy, huh?
SAVING AN IMAGE
1. In the menu bar click Web/Image Optimizer.

2. In the pop-up box you will be able to choose between saving as a jpg or a gif.
    To save as a transparent gif (to be used in an animation, dark background or personal preference), check the box next to Transparency. In the pop-up box you have two options. Choose Selected objects to save the selected object/s. Choose Entire image if you want to save all the objects and the background. Click Save As. In the example below, I chose to save it as a transparent GIF.
   

    If saving as a jpg, to optimize the image file size decrease the Quality to the point where your picture degrades/loses clarity and then increase the number two or more until it looks nice again yet keeps the overall file size down. You can see the file size at the top of the screen. Click Save As.

3. In the next pop-up box, select the folder where you want to Save your file and give your file a name.
   

For more information about the various image formats and their uses, click here.
A special thank-you to MaryLou for her input into this tutorial.