first off if its some sort of business website you should tell the client that you are completely inexperienced and give them a chance to hire someone who knows what they are doing vs risking you killing their website.
if they still want you to figure it out you should start by learning the language (html, php, mysql and in that order you cannot go wrong). learn how to use a ftp program (filezilla is good and free. i use fireftp from my browser on occasion - i use firefox - and i'm also a fan of smartftp and flashfxp).
taking up management of an existing website can be tricky. you need to know (or be able to recognize) how the website was made. is it a website with static pages? did they make it with dreamweaver or some other gui type editor? did they simply whip it up in a text editor? is it a more dynamic site using a content management system (cms) like drupal or joomla? did they customize blogging software like wordpress? there are just too many variables for me to give you an adequate answer but those questions are definitely something you need to find out or discern for yourself.
also as far as a password protected directory it depends on what software they are using for the website and just how its protected (via .htaccess maybe or something controlled by the cms?). if you have credentials to log into the account via FTP or SSH you don't even really need to know it though. is there some reason the client didn't tell you the password for that part of the site? you might not want to reset it if it is widely used by the company, might just ask the client what it was.
now you can log into the dh panel and use the webftp (go to manage domains and you would see the link under the domain name) and download any files for editing. i would recommend that you get your own ftp program and learn how to use it. for code editing notepad would do the job if you had nothing else but I use Editpad for my text editing needs. the lite version is free but the pro version has more bells and whistles that appeal to me. i hear notepad++ is great too though and completely free.
i know my post is a bit long winded but i cannot stress enough how important it is for you to learn the lingo. you should have a good understanding of html at least. i am sure you can get books on it at your local library if you don't want to purchase any. also there are tons of online resources if you look for tutorials. i learned everything i know about web development online without paying a cent. you do not necessarily need to have any php or mysql skills if you are using a cms but it would help greatly in case you have a need for some advanced troubleshooting if the website does use something like that. start learning how to make pages and what not first before you go mucking about on a website you didn't make, especially if it is already 'live'. ignorance is not bliss when it comes to this sort of thing.