I'm not on Charter but here is what normally applies:
First be sure that your system uses SDV. If not you don't need a Tuning Adapter.
You need one TA (Tuning Adapter) for each TiVo.
You connect the USB port on the TA to a USB port on the TiVo.
The TV cable from the wall plugs into the TA. A short coax cable connects from the TA to the cable input of the TiVo.
TA kits come with the short coax cable and usb cable that you need.
Here is the Charter web page on CableCARD (and TA) self-install:
Normally the TA is free and you can self-install at no charge. Even if you end up buying your own coax or usb cable, it should be much cheaper than having a service call for the installation.
The common troubleshooting procedure for TA's is to power cycle them while disconnecting the USB cable. When the green light goes steady on after a few minutes, reconnect the USB cable and the TiVo should go through its acquiring channels procedure for a minute or two. Sometimes you also have to restart the TiVo in conjunction with this.
Anything but a steady light means the TA has some issue. A sequence of 8 blinks-pause means the TA isn't authorized. A sequence of 6 blinks-pause means it's not communicating with the TiVo via the USB. This is for the Cisco STA1520 TA's which I believe Charter uses. There is a reset button on the front of the TA but I don't use it as I believe power-cycling is the more reliable reset mechanism.
The most common problem with TA's is occasionally losing some or all of the SDV channels, which is usually fixed by the reset procedure just described.
Good luck. Some of us find TA's a far from reliable device.