1. The backdrop: My favorite material for white backdrops is white marine vinyl. It is heavy, durable, washable, and as you can see, it photographs well. I have about 4 yards of white marine vinyl from JoAnn's. I can hang it or lay it out as needed.
2. The lighting: The best lighting is outside on an overcast day. Sometimes you need to recreate that. On blustery days, I have been able to set up in the sun and wait for intermittent cloud cover. Shooting in full sun is no good because the shadows are too harsh. Sometimes I have to settle for the shade. Having a truly white backdrop comes in handy when you have to use shade or even indoor lighting - see the next tip.
3. Post production: GIMP is a free program that works a lot like photoshop. In GIMP, click on color, then levels. In levels, I choose the white dropper which is on the right, then click a spot on the white background to tell it what is white. (Shooting in the shade, the white area may photograph grey. Shooting inside, white may appear yellowish.) This will smooth out the white background and make it pop. You can play with clicking different spots on the photo to get it how you want it.
I never thought to photograph animals this way. Strawberry wandered into the weed photoshoot. I will set up again and get some more shots of cats on white. Everything looks so fresh on a white background.