Some good advice there Rob. All these years of landscape photography and I have forgoten something as basic as the exp. adjustment.
Anyhow, hi Niko. I had a web look at your camera and it seems much like mine (Olympus 410). You actually do have some shutter control, which is the settings wheel, which I assume yours has. (Program Auto, Night Scene c-3sec. and Beach & Snow, fast speeds, being my most used, with flash as Rob suggested.) I have included two shots taken hand held with these methods just to show what is possible. And practice a still hand!!
Above all take lots of pics(the beauty of digital) and have fun.