The best place for advice on getting started with APIs and Mashups is programmableweb.com - they've got lots of HowTo guides and the biggest API database on the web. They also have tons of examle Mashups to browse.
Also, if you use Wordpress, check out the WP Robot plugin. It pulls in Amazon, eBay, Commission Junction, Yahoo Answers, Flickr, Articles, Press Releases. and lets you Mashup data. It's really meant for auto-blogging (kind of spammy) but certainly works with lots of APIs and would be a good way to see what you can achieve without spending an eternity learning it all yourself.