The bare minimum to wash your windows like a professional window cleaner would be a scrubber and a squeegee. The scrubber applies a soap and water solution to the window to agitate dirt and the squeegee removes it all–leaving behind sparkling clean windows.
That said, there are a number of other products that can make the process of cleaning windows quicker and easier:
Your individual needs and preferences will affect what tools will be most necessary or useful to you. There are also a number of pre-built window cleaning kits available. You can use them to buy what you need to get started or give you an idea of what tools are most popular.