There are many ways to connect/access/use a BeagleBone Black. The easiest way is with a USB cable, but there are times you'll need to use one of the other methods described below.
To connect via USB, refer to BeagleBoard.org's Getting Started page. Below are a few points not covered in the guide you may need to know depending on your OS.
It is also possible to access your BeagleBone by plugging it into a router/network and navigating to the assigned IP address. This method works well on networks over which you have control so that you can assign/associate an IP address with your BeagleBone's MAC address (otherwise it's difficult to determine your BeagleBone's IP).
If you have an HDMI monitor/TV, a Micro-HDMI to HDMI Socket Adapter Cable, and a USB hub, you can setup your BeagleBone as a desktop computer. One of the Accessories is LXTerminal. In order to keep from having to preface all of your commands with sudo, run the following:
I don't usually connect to the BeagleBone via the serial debug pins, but it is possible, and would be useful in the event you messed up your network configuration file and don't have the hardware on hand to set it up as a desktop computer.