Web based aggregators such as Bloglines and Google Reader are particularly popular with teachers because they let you check your feeds from any computer, while aggregators like NetNewsWire (Mac) or FeedReader (Windows) have more options--but are limited to a single workstation.
iTunes (Windows or Mac) includes an aggregator for subscribing to Podcasts.
Most aggregators have a subscribe button of some kind. Generally, all you need to do is locate the web address of the RSS feed (see the tip below), copy the address, click on the subscribe button in your aggregator, and then paste in the address. From then on, any new updates will appear in your aggregator and save you the trip back to the website.