Normally, a child theme should be used when developing any website with a free or commercial theme. It’s actually a very simple process, although it changed slightly about a year ago, so recent instructions are important. The Child Themes page in the WordPress Codex has the essentials. WPMU.org has a good tutorial which goes into a lot more detail.
There are exceptions; for example, with purchased child themes like those offered by StudioPress; you can’t make a “grandchild theme”. When in doubt, check with the author of the theme you’re using as to whether a child theme is the recommended way to go.