Open source scripts and programs
Before I get into the meat of this article -- using public APIs in your Web applications -- it's worth mentioning the existence of open source scripts and programs. Without getting too deeply into detail, open source is a term used to describe code that can be, to some degree, freely used and reused in your own applications. Consult Resources for relevant links, but at a 10,000-foot view, you can take open source code that someone else has written, and simply drop it into your own environment, without charge or (much) restriction.
If you make use of open source code, sometimes you'll have to add some extra documentation to your applications, or perhaps contribute changes you make to the open source program or script back to the community. Whatever the particulars of the program that you use, the end result is that you can use code that you didn't have to write, and perhaps wouldn't have been able to write without a lot of help and resources that you don't have. Projects like Apache make it easy to take advantage of the work that others have done -- and don't worry; they want you to use their work!