I\'m trying to develop an Android app for browsing a Wordpress-powered blog I own. I\'m trying to figure out how to retrieve posts and other information from the blog to display
Yes, it can be done.
One way is to use the xml-rpc api. Wordpress blogs have an xml-rpc api(which you need to enable on the Wordpress blog under "Settings - Writing"). You will also need to create a user on the blog, which you give at least read access, and for which you include the credentials in your app. From then on, you can do xml-rpc calls to your Wordpress blog(s).
If using this xml-rpc api is an option, take a look at this Java lib: http://code.google.com/p/wordpress-java/
You can get the blogposts using this lib like this:
String username = args[0];
String password = args[1];
String xmlRpcUrl = args[2];
Wordpress wp = new Wordpress(username, password, xmlRpcUrl);
List recentPosts = wp.getRecentPosts(10);
Also, the official Wordpress Android app is open source. Instructions to get it are at: http://android.wordpress.org/development/ You could use this source code as a starting point and adapt it to your needs.
Note that you can only use the xml-rpc api when you have a user with read access. If you do not have the credentials of a user with read access, you can't get the posts using the xml-rpc api. Fetching the rss feed and parsing the rss feed with some java lib would probably be your best bet then(check http://www.vogella.com/articles/RSSFeed/article.html on how to read an rss feed using Java).