Rock salt is a great way to melt ice, but it's not the only one. Check out these five homemade ice creams made with items you probably already have at home. It's a bit inaccurate to say that salt melts ice, although this is definitely how things appear at temperatures close to normal freezing. It is more accurate to say that salt lowers the freezing point of water and does so when it dissolves.
It's not just salt that can do this; any substance that dissolves in water lowers the freezing point. However, because rock salt granules are larger than table salt granules and contain more insoluble impurities, they don't dissolve as well and don't lower the freezing point as much. The answer is yes, table salt is great for melting ice. While rock salt is the most common form used on icy surfaces, you can also use table salt.
In fact, table salt is more effective because, thanks to its finer grind, it has more surface area that will come into contact with ice. The more salt the ice touches, the faster the ice will melt. Applying salt to already formed ice will only have a noticeable effect once the affected areas have seen some traffic (whether they are boots or tires that step on the salt against the ice), so the first ones that cross will be subject to icy conditions regardless. If you want to prevent ice from building up on your windshield, try spraying it with a mixture of water and vinegar; while the mixture doesn't melt the ice, it can help ice to form first if you spray it with it the night before.
Add some dish soap to the ice melted with alcohol and it will reduce the chance that the melted ice will freeze again.