To get to the internet: Network Address Translation (NAT) is the simplest way of accessing an external network from a virtual machine. A virtual machine with NAT enabled acts much like a real computer that connects to the Internet through a router.
To get to your computer: No physical adapter is required. Host-only networking creates a network containing the host and a set of virtual machines, without the need for the host's physical network interface.
To get to the rest of your network: Bridged networking looks to the host system as though the guest were physically connected to the interface using a network cable. The host can send data to the guest through that interface and receive data from it. This means that you can set up routing or bridging between the guest and the rest of your network. For this to work, you probably need a device driver on your host system.