Have they been using a content management system to maintain it, or just manually doing it with a text editor? If they use a CMS then you will have to do likewise, or else any change they make later will undo whatever you've done. By 'help' I'm assuming you won't be the only one working on it.
If you'll be manually editing the files I would recommend Notepad++. Actually I recommend Notepad++ to replace Notepad anyway. And you will need an FTP program to upload/download files. Or if they require a secure login, which they should, you could use something like WinSCP, to give you a secure shell login plus it provides an Explorer or Commander type interface.
For HTML help you can just Google anything you have a question on, all the info you need is out there. w3schools is a good place to start if you're just learning or need reference material.