Typical methods using a VPN to securely connect from your environment to Azure is as follows. Setting up VPNs is not a simple process and takes time. See the Azure Documentation Center.
|Site to Site (S2S)||Connect by creating a site-to-site VPN gateway connection from your on-premises networks to Azure VNets.|
|Point to Site (P2S)||Connect by creating a point-to-site VPN gateway connection from your virtual network from an individual client computer to Azure VNets. If you have only a few clients to connect to a VNet, use P2S instead of S2S.|
|ExpressRoute||Connect from an IP VPN network, a point-to-point Ethernet network, or a virtual cross-connection using an Ethernet exchange through a connectivity provider.|
You can set up a jumpbox, but it is not as secure as a VPN until you secure it with SSL.
After deploying a solution template, you can create public IPs if you are connecting to the public cloud through the Internet.