Rump steak comes from the back end of the cow. The rump muscle is lean because it's heavily used in the cow's day-to-day activity. The leanness of the meat makes it prone to drying out, and precautions must be observed during preparation to keep your rump steak moist.
Marinate your rump steak with your favourite marinade overnight in the fridge to help keep it moist when you cook it. Use a soy-based marinade, teriyaki, garlic, chipotle or something simple like red wine or beer. Skip this step if you prefer your steak served without marinade.
Remove the steak from the fridge and allow it to warm to room temperature. Preheat your pan on medium high.
Add enough olive oil to the pan to coat the surface and add the steak. Sear the outside of the rump steak to a rich brown colour to lock in moisture.
Turn the steak only once as it cooks, and avoid using a fork to pierce the flesh and allow juices to run out. Cook between medium-rare or medium to ensure it doesn't dry out. Medium-rare has an internal temperature of 60 degrees C (140F). Let this drop by a degree or two if you like your steak very rare.
Remove your rump steak form the pan and let it rest on a plate or cutting board for several minutes. Slice it with a sharp knife against the grain so the meat will be tender.
Rump steak can also be braised slowly in a cooking liquid like wine or stock to help make it tender. You can braise in a large saucepan, a roasting pan or in a slow cooker.