Hello - I am too a personal owner of a CASIO CTK keyboard, a little older than yours (model CTK-601) a great keyboard BTW, and I have connected it to my computer successfuly.
There are 2 ways of connecting the keyboard to your PC......Using the MIDI outputs and a special MIDI to gameport adapter - if you have a very old system and have a joystick port (D-sub shape) on your soundcard or PC, then you use that cable. Of course this is legacy and stopped existing in newer computers, now USB is used.
Only the professional line of soundcards have direct MIDI inputs. For most of us, with consumer soundcards and PCs, there are no MIDI inputs.
The good news is that newer keyboards support USB MIDI and features direct USB connection - so all you have to do is install the drivers that are provided with your keyboard, usually a CD, and follow the instruction to install the USB drivers for your casio keyboard, BEFORE you plug in the cable (very important!) once installed you reboot and connect your keyboard using a USB cable
Now if your keyboard is older and has MIDI outputs, like mine for example, you will need to purchase a MIDI to USB adapter, those have MIDI cables in one end that plug to your keyboard and the other end a USB connector....... I don't know about the rules if I am allowed to post websites, but the product i'm using is the Uno from M-Audio - in google do this search:
(exactly as shown above with quotes, and uno outside quotes)
Your CTK-810 may alreayd have a USB connector on it, as it is a newer generation keyboard - I am pretty sure it does - what you will have to do as stated above is located your bundled CD-ROM and install the USB drivers - you will need to purchase a USB cable (seperately).