Basic Setup Questions

I’m pretty new to WP, I have a previous site (www.jocce.se) that I’ve gotten a lot of help building. This time trying to learn stuff and make it by my self, since the WP-platform seems to be really easy to work with!

I’ve just set up a test site:
http://test.båglampan.se/
(Might work better with: (Because of the Swedish letter…)
http://test.xn--bglampan-9za.se

I’ve set up the pages, “Lediga Lokaler” and “Hyresgäster” are going to be showing posts in category “Lediga Lokaler” and “Hyresgäster”.
How do I set this up?
Right now it’s just an empty page, and need to know how to make these pages show the posts?

/Jocce