You can connect to your VPC in a number of ways, two examples:
You can connect to instances in your VPC via VPN (over an Internet Connection).
You could also use Direct Connect to connect to instances in your VPC via a private network (ie NOT over the Internet).
Better ping/response times (more reliable)
More secure (as it bypasses any and all Internet traffic)
More costly (there are setup/ongoing charges with Direct Connect)
VPC & Peering
Also have a look at peering for communication between VPCs.
Connect privately to other VPCs- Peer VPCs together to share resources across multiple virtual networks owned by your or other AWS accounts.
Direct Connect & VPN
Setting Up AWS Direct Connect with VPN http://docs.aws.amazon.com/govcloud-us/latest/UserGuide/setting-up-direct-connect-with-vpn.html