First, test your water. Is the smell constant, or does it come and go? A simple home test kit can tell you how much sulfur you're dealing with. Don't guess when you can test.
If the smell is mild and only in hot water, the issue might be in your water heater's anode rod. Replacing it with a special aluminum rod can often solve the mystery without any fancy equipment. It's the cheapest trick in the book.
For strong, persistent smells from every tap, you'll likely want a whole-house system like aeration or oxidation filtration. Call a local water pro—they're like plumbers with a cool science kit.