I have a sprite image set as the background of an element on my page, but how do I find the proper offsets so I can actually see it on the screen?
When you build your sprite image in your graphics program you have to write down the offsets for each element and use those in your CSS.
There are web tools that will create the sprite and give you CSS with positions for you. http://css-sprit.es/ is an example.
The online CSS Sprite Generator is worth looking into, it should take some of the tedium out of this approach.
The main thing to remember is that the offsets will be negative. If you have an image that's 100x500 with 100x100 sprites, then the offsets will be:
.img1 { background-position: 0 0; }
.img2 { background-position: 0 -100px; }
.img3 { background-position: 0 -200px; }
.img4 { background-position: 0 -300px; }
.img5 { background-position: 0 -400px; }
Since empty areas of a png file takes up very few bytes, just put all "images" at a regular interval, say every 50 or 100 pixels. That way you can simply find the first proper value and remove 50/100 pixels from that (50 ctrl-x in vim).