When walking on ice, it is very important not to walk too quickly and to wear shoes with good traction. Many experts also suggest that people can avoid injury by taking short mincing steps instead of long strides that carry too much weight. Point your feet slightly outward. Watching the ground while walking on ice can help you avoid particularly dangerous areas, and that can be crucial to preventing a fall. Another important consideration is to avoid walking on ice in frozen lakes because of the danger of breaking through the ice and drowning or suffering hypothermia.
Walking carefully and mindfully is a lot of help when walking on ice, and good shoes can give you a little bit of an edge. Shoes with a lot of traction on the bottom can sometimes help you avoid falls, especially if that ice is covered in snow that the shoes can dig into. Some shoes can help in the same way that snow tires help when driving. Ice is sometimes so slippery that good shoes aren't enough, but a small improvement is generally better than nothing.
Hills are especially treacherous when walking on ice, and it is generally better to avoid them if you can. When you are forced to walk up a hill, look for a way to do it that doesn't require you to actually move up a slant. For example, stair steps would generally be much better than some kind of steep incline.