With font icons you include font file that are of the extension .woff, .ttf, .eot, .svg and the css file for that font. They are less in size and and you can change the size of the icon when required, with image files png/jpeg it distorts the image file, where as font icons scale properly.
With multiple images you have to make multiple http request to the server, which can be avoided here.
The font icon files are also available on cdn hence you don't have to request it from the server if some earlier website has it already cached it in your browser.
With fontello you can customize and use only the icons that are required.
There is also fontawesome current version 4.2 where you can get the font icons, if you need support for older version of browsers you can opt for old version no 3.
You can also customize it using LESS/SASS.
Another option is using css sprites you can optimize it using traditional methods or using online services.
Using it in html is pretty simple, once you make sure the css files and font files are loaded in the browser you just need to add class name to the html element and you are good to go, you can then customize the font size, color, background color as per your wish.