No matter how safely you drive, you won't get very far without good traction, and good traction starts with good tires. At a minimum, make sure your tires are properly inflated and have plenty of tread left on them before you drive on icy roads.
If you'll be spending significant time driving on ice, you'll likely need to switch to snow tires every winter. Snow tires are made of softer rubber than all-weather tires, which gives them a better grip on the road. In addition, snow tires have specially designed tread patterns to provide better traction on ice and snow. Some snow tires even have the ability to accept metal "studs" for additional traction in certain situations, although these studs are banned in some areas since they damage roads. Snow tires will wear out quickly in normal driving conditions because they're made of softer rubber, so make sure to switch back to all-weather tires once winter has passed.
Snow chains are another way to get better traction on icy roads, and since you can keep a set in your car at all times, they can be a lifesaver if you find yourself caught in a snowstorm. With snow chains, however, you won't be able to drive faster than around 30 miles per hour (48 kilometers per hour).
Lastly, cars with four-wheel drive (4WD) can hug icy roads better than those with two-wheel drive, though even 4WD cars will need snow tires or chains to handle more extreme winter weather.
Even with a properly equipped car, driving on icy roads is still a dangerous proposition, which is why states invest millions of dollars in plowing streets and highways, as well as covering them with salt and sand. Salt and sand are often used together to improve road conditions since they each provide a different function in improving traction. Salt dissolves into icy roads and actually lowers the freezing temperature of ice, while sand provides a gritty surface for tires to adhere to.