Any plain text editor. Windows Notepad will do, but there are many text editors specifically geared toward writing HTML, which can save you a lot of typing.
Go to your favourite search engine and search for "html editor"; you will get LOTS of matches
Whatever you use, the HTML must be saved as plain text, and the document must have the extension .htm or .html.
The World Wide Web Consortium has a page of browsers and authoring tools.
Any web browser. A web browser is just a program (software) specifically made for viewing web pages. Examples of web browsers are Microsoft's Internet Explorer (not recommended because of security problems), Firefox, Opera, Safari, and, well, there are lots of them. Most are free.