Azure VMs can connect to each-other out of the box if they are in the same Cloud Service. Then, you can enable network file sharing and share files between them normally.
Please see here for instructions on how to create VMs in the same Cloud Service.
If the above is correctly set up, you can access one VM from another via its hostname. So if you have a VM called "vm123" and a folder "shareXYZ" which that VM is sharing on the network, other VMs in the same Cloud Service will be able to access it at "\vm123\shareXYZ", as you would expect.