How to PuTTY into a VirtualBox VM with a NAT network adapter?

You can use the address of the host, e.g. 127.0.0.1 if you are on that machine. You will need to set up port forwarding in VirtualBox, which can be found in the networking settings:

Set up the rule using whatever host port you want (as long as it doesn't conflict with another service on the host), and whatever your guest IP and port values are, for example:

(If you leave the host IP field blank, you will be able to access the guest from any machine on your LAN.) Then you can ssh to your local IP on the specified host port, and the traffic will be forwarded to the port you specified on the guest.