Removing a white background with Replace Color:
Go to Edit > Replace Color, use the eyedropper to set the 'Source Color' to white. Keep the 'Target Color' empty for the white to turn transparent. Go to the Save menu and choose PNG.
Removing a white background with Cutout's Magic Brush:
Go to Edit > Cutout, and choose the Magic Brush selector. Make sure it is set to 'Remove'. Adjust the brush size and tolerance depending on your image. Carefully click and move the brush around the image and you'll see a red mask follow your brush to remove the selected area.
Press the blue checkmark to apply. Choose if you'd like to 'Trim Transparency' to remove the excess area around your subject, or if you want it exported as separate layer in your Image Manager. Save your image as a PNG.