Comet 2011 L4 (PanSTARRS) makes its closest pass by Earth on March 5, but at this point it will still be mostly a southern hemisphere object. PanSTARRS has already been showing itself to southern hemisphere observers (along with another comet, Comet Lemmon, which will enter northern skies in April). Try looking to the southwest right after sunset each evening in March.
After March 5, the odds of spotting the comet become better as Comet PanSTARRS moves higher into the sky and brightens. The current brightness estimated for PanSTARRS is around second or third magnitude, similar to the stars in Cassiopeia, the W-shaped constellation above and to the right of the comet. Once the comet rises 15 to 20 degrees above the horizon, it will move horizontally across the sky, passing from the constellation Cetus into Pisces. It passes closest to the sun on March 9/10. On March 12 the comet will lie to the left of a crescent moon and a more-difficult-to-spy Uranus only half a degree below, and on April 3/4 the comet skims past M31, the Andromeda Galaxy.
Saturn enters the late evening sky in early March with the moon lying beside it on March 1 and the star Spica close by. The moon returns to Saturn by the end of the month, slipping in between Saturn and Spica on March 28 and displaying a fat gibbous phase. The full moon occurs on March 27 at 2:27 a.m. PDT.