There are several modes for network connections in VirtualBox; I'll describe just 2.
NAT processes all network requests from the VM and communicates them to the internet. You will not be able to access the local network except by IP Address (if even that) because it will usually be on a different subnet, network, etc.
Bridged Networking causes the VM to use your network adapter directly. This allows it to communicate on the network more easily because it will appear as if your network adapter has two computers running on it. This is necessary to run the guest as a server or to read files off the local network. I've had to use this to run shared files on my host PC inside the guest PC to test them.
TL;DR: Just internet access? NAT should be fine. LAN access from inside the VM? Try bridged networking.
On the VM Settings, open Network Adapters.
Using NAT (the default): Select NAT and press OK.
Using Bridged Networking: Select Bridged Adapter, and select your network adapter from the list. Then press OK
If both of these don't work, you have a different problem (such as a firewall blocking the VM.)
