Insulation work, like painting, is a job that lends itself to doing it yourself. There are a lot of different types and thicknesses of insulation, so before you embark on this project you really need to do a thorough assessment of your home to determine where new insulation is needed and what type to use. For a rundown of the different types, you can find a lot of information here.
Once you have determined the appropriate places to put the new or replacement insulation, you need to figure out how much you need and get it. Installing it in an attic, while it can be uncomfortable and awkward if the attic is not floored, can be done relatively easily.
It is when you need to put in in the crawl space that things get messier. Crawl spaces are typically cramped and dirty. You might want to consider putting down a vapor barrier (heavy duty plastic) on the ground before starting. You can either tear out the old insulation or place the new insulation over the old. Typically the insulation comes in rolls with a paper edge you can staple to the joists. The joists are usually either 18 or 24 inches apart, so you need to get the right size insulation for the area you will be working on.
You will need a mask and safety glasses to keep the fibers, dust, and dirt out of you nose and eyes while you are doing the work.