Supporting your clients is one of the most responsible and important aspects of your online commercial activity. First of all its a vital tool which allows you to keep in touch with your customers, to study their needs and hear advices or abuses. And what is even more useful - to increase sales and make your customers return. We are not the first who state that personal communication contributes to understanding of mutual needs and thus leads to enjoying clients confidence. Its definitely a reliable way to make your customers happier and your incomes growing.
Ok, enough of theory. Lets think of how to put it into practice and not to give an arm and leg to your supporting company.
We dare to suppose that there are 2 ways to support your clients online. The 1st one is to get your own Support Department, the second one is to use Supporting Service(outsourcing as a variant).
If you are going to provide support by yourself you will definitely need some communicational software like live chat and ticket system. The only decent OpenSource Free software that satisfies both these functions is Help Center Live 2.0.6. It includes core Live Chat engine with a number of plug-ins including OsTicket module which allows to receive and handle support tickets.
At your initial steps you will be able to create your FAQ Database and study needs of your clients.
The software mentioned above will enable you to track operators statistics, run several departments and much more. Here is a list of available features:

Brief Feature Review
Unlimited Operators
Unlimited Departments
Unlimited Users
Real-Time Chat Sessions
Real-Time Visitor Monitor
Unlimited Chat Sessions
Initiate Chat Sessions
Assign Operators to Mutiple Departments
View User’s Information
Operator to Operator Chat
Per Department Status Icons
Request Polling
Collect Visitor’s Information
Track Visitor’s Footprints
Track Visitor’s Referrer
Typing Notification
Display Operators Picture in Chat Windows
Autosave Chat Transcripts
E-mail Transcripts
Print Transcripts
Hot Pages
Transfer Files
Transfer Chat Session
Canned Messages
Canned Commands
Push Web Pages
Leave a message
Toggle sounds on/off
Toggle status online/offline
Implementation to your Website
Plugin Modules
Modify the Source
Runs on your server
Fully Customisable to fit your Website
For sure you can use any commercial software but as we stand on Open Source positions we recommend free soft.
If you think of your expenses optimizing then you should take a look at outsourcing Supporting Companies, usually these guys give you a good chance to save a bunch of dollars on tax, office and personnel expenses. Why paying $3K to some guy (we do not include taxes and office expenses) if you can get 24/7 support for less? Yep its one more thing for pondering.