Look, you are asking for stuff that or you have the necessary skils to build, or you must use a free script.
If you use a free script, either a script in a zip file for you to upload and configure yourself, or in the other way, you want one of those free services where you just copy and paste a code and you will have everything you need with no trouble at all, even so, you need some knowledge, at least knowledge in html, php, configuring/creating a mysql database, perhaps even the tables names if the script has does not have a dynamic install script.
Like you see, even if you do not want to build the script yourself, you must have knowledge of quite a lot of things, not just programming languages, a lot more.
In my opinion, and from what i just read from your topic content and replies too, you want a messenger for your website, well, cool messenger are not free, so forget it, you might want free chat, and as a matter of fact, i am about to insert one for my blog/website, which is free, and it is extremely cool and perhaps even has more then you want, so here it is:
Blueimp.net - Free Ajax Chat
https://blueimp.net/Screenshots:



Features:
QUOTE
Easy installation
Usable as shoutbox
Multiple channels
Private messaging
Private channels
Invitation system
Kick offending Users
Ban offending Users
Ignoring offending Users
Online users list with user menu
Emoticons / Smilies
Easy way to add custom emoticons
BBCode support
Optional Flash based sound support
Optional visual update information (changing window title)
Clickable Hyperlinks
Splitting of long words to preserve chat layout
Flood control
Possibility to delete messages inside the chat
IRC style commands
Easy interface to add custom commands
Possibility to define opening hours for the chat
Possibility to enable/disable guest users
Persistent client-side settings
Multiple languages (auto-detection of ACCEPT_LANGUAGE browser setting)
Multiple styles
Chat window adjusts to browser window with included styles
Easy layout customization through stylesheets (CSS) and template system
Automatic adjustment of displayed time to local client timezone
Standards compliance (XHTML 1.0 strict)
Accepts any text input, including code and special characters
Multiline input field with the possibility to enter line breaks
Message lenght counter
Realtime monitoring and logs viewer
Support for unicode (UTF-8) and non-unicode content types
Bandwidth saving update calls (only updated data is sent)
Optional support to push updates over a Flash based socket connection (increased performance and responsiveness)
Survives connection timeouts
Easy integration into existing authentication systems
Sample phpBB2 integration provided
Sample phpBB3 integration provided
Sample MyBB integration provided
Sample PunBB integration provided
Sample SMF integration provided
Sample vBulletin integration provided
Separation of layout and code
Well commented Source Code
Developed with Security as integral part - built to prevent Code injections, SQL injections, Cross-site scripting (XSS), Session stealing and other attacks
Tested successfully with Microsoft Internet Explorer, Mozilla Firefox, Opera, Safari and Konqueror - built to work with all modern browsers

Requirements:
QUOTE
Server-Side:
PHP >= 4
MySQL >= 4
Ruby >= 1.8 (optional)
Client-Side:
Enabled JavaScript
Enabled Cookies
Flash Plugin >= 9 (optional)
The client-side logic is written in JavaScript. The server-side logic is written in PHP. The chat messages are stored in a MySQL database.
The Flash plugin is used for (optional) sound support and to establish the (optional) socket connection on client side. The (optional) socket server is implemented in Ruby.
Documentation
http://ajax-chat.wiki.sourceforge.net/http://sourceforge.net/docman/?group_id=214758
Comment/Reply (w/o sign-up)