Find a large copper, stainless steel or glass mixing bowl, and make sure it's spotlessly clean. Plastic bowls can harbor grease, which will prevent the egg whites from forming stiff peaks.
You'll need measuring spoons and measuring cups, and a small bowl or pitcher to place the egg whites before adding them individually to the mixing bowl. Having an interim bowl saves tossing all your egg whites if some egg yolk slips through.
You could whisk your eggs by hand, but I don't recommend it. So use an electric mixer, and again, make sure the beaters are clean.