well...basically for a start you can try :

potrait - aperture priority mode. use wide aperture (small f-no like f/2.8)
landscape - aperture priority mode. use small aperture (big f-no like f/8)
night shot - shutter priority mode. use slow shutter speed (1/15 ~ 15 sec depending on effect you want & how dark it is & use tripod)

i should add that with a compact cam like this, you won't get any good bokeh (ie shallow DOF) even with widest aperture of f/2.8 unless your background distance is great