Just to follow on from tcv (get the manual from his answer). With the KX-TD and newer KX-TA Series (this includes the 308) you'll need to...
- Go to the main console (extension 101) and put it to programming mode by moving the switch on the phone to programming position.
xxxx is the password for programming). This is usually
9999. If you don't know the password, ask the company who installed the PBX.
-  - RS-232C Communication Parameters: CR+LF, 9600, 8 bits, mark parity, 1 stop bit.
-  - Choose 0 (skip perforation) - unless you want holes in your PC ;-)
-  - Incoming on and outgoing on
-  - Choose to print the speed dialing
-  - Choose account code report to be code or index.
-  - Choose English language reporting
- Move the programming switch to the original position
Now all you have to do is hook it up to your PC using a serial cable, and then the PBX can send SMDR (as bogdan mentioned). Remember that for other PBX models this process will be different, but you'll be aiming for basically the same goal. The manual will usually tell you how to set up SMDR.
Here's some SMDR data from the same model as the OP (Panasonic KX-TA308):
Date Time Ext. CO Dial number Duration Code
4/16/03 5:24PM 101 02 2110024 00:02'19" ....
4/16/03 5:26PM 101 01 2423942 00:00'00" ....
4/16/03 5:27PM 101 02 2105483 00:00'13" ....
From Jon's comment...
You just need a serial cable, you
might need a 25(?) pin to 9 pin
converter though. 308 & 624 are
designed to be programed through the
first handset - typically 201 as
mentioned. Newer systems do have USB
programming In the UK at least these
ones are called TEA 308 & TES824s)
Like Jon said, the newer ones can be programmed from a PC via USB (specifically, the KX-TDA series: KX-TDA30, KX-TDA50, KX-TDA100, KX-TDA200). In some cases we can also use the USB connection to receive SMDR data, but you'll need a 3rd party driver to do that. For the KX-TDA's, the program to use is the
KX-TDA Maintenance Console (but for the OP's PBX, we must use the handset method as described at the start of this question).
As for the software to view the data, the term you're looking for is called "call accounting" or "call logging". Something like PhoneJournal* should do the trick. Remember that call accounting/logging not to be confused with "call recording", which is something completely different.
*Disclaimer: I work for a company that sells this product, so you should of course review other products.