Typically the call management system you're thinking of involves (1) some setting up of specialized telecom lines, (2) the installation of call monitoring/routing hardware, and (3) the development or purchase of call monitoring/routing software.
You would generally get the hardware
here. (Dialogic is now part of Intel, btw). Some companies (like my former employer, which I would rather not name) work at integrating Dialogic hardware into running, tested, fault-tolerant rackmount servers. Other smaller players (like Aculab and Pika) also manufacture hardware to compete directly with Dialogic. Generally all of this hardware can be used in industry-standard PCs, as long as you observe the power and cooling requirements.
For the software, you would generally either write your own, outsource to a company specializing in (very expensive) bespoke computer telephony software, or get a pre-rolled solution. The two big pre-rolled solutions I remember:
Artisoft Televantage--also nicknamed 'Teledisadvantage' because it was quite a piece of shyte. It came with an extremely broken installation routine that never worked like the instructions said it would, and if you didn't do the technical equivalent of sacrificing a goat during software installation, you'd blow it out of the water and have to go back to square one (sometimes reinstall the entire O/S). Needless to say, we didn't sell many copies of that.
Enterprise Interaction Center--EIC for short. It's a large, extensible,
very expensive (somewhere in the six-figure realm IIRC) mater-and-pater of all call management systems, developed by Interactive Intelligence, Inc (I3 for short). It practically even makes the coffee for you in the morning. Most people who use it barely use a tenth of its full capabilities (some never even change the default on-hold music

), but they still buy it for the simple reason that it's often still cheaper than bespoke software.
Dialogic makes development for their products fairly easy by providing an SDK as part of their drivers. The Dialogic SDK and drivers are available for Windows platforms, SCO OpenServer/UnixWare, and Linux (and perhaps other platforms by now). Cross-brand portability of this software (i.e. taking binaries or source code written for Dialogic SDK over to Aculab SDK) is pretty much nonexistent. Last I heard, Dialogic was creating a software package called "CT Media" partly to address this portability problem.
When you integrate all this together, it's actually pretty cool. At my last job, we were running an EIC server with a few Dialogic T1 and fax boards, plus EIC clients on all the workstations. We could actually receive voice mails in our inboxes--whenever someone left a message on my phone, I'd get an e-mail in Outlook with the message embedded as a PCM audio stream I could play back. Same went for faxes; they got routed to our inboxes as scanned images. It may have even integrated with our Pivotal CRM software (i.e. you could pull up a contact in Pivotal and maybe double-click on it to dial the contact number). And of course, the basic call management stuff (caller ID, mouse-click to put on hold, etc.) was all there.