how can i do long exposure shots?

[roi]

Hey guys,
I've been trying to do long exposure shots over the weekend but I couldn't figure out how to. How do I get it to go beyond 30secs? I did bulb but all I get is a black image. And what is mirror lock up? I see it as a feature but have no clue what it's for. Sorry for my ignorance about this, but I just started exploring more features I've never used on my D40/D80. Thanks!