Your question is rather generic. You could elaborate further.

To start with, VMMs or what are generally called hypervisors handle many tasks relating to sharing of physical resources among virtual machines. They enable low-level hardware- or platform agnostic details to be abstracted from the VM and host OS. How they work depends on the type of virtualization (hardware, para, or OS virtualization) and the vendor (VMware, Hyper-V, Xen, Docker, etc). 

In general hypervisors are responsible for scheduling of virtual resources such as VCPUs, storage, and network. Though memory is not really virtualized (not shared), they statically partition memory pages among VMs and manage the caching and paging on behalf of the VMs. Another aspect of memory management by hypervisors is memory balooning (enabling memory allocations to VMs shrink and grow is needed).  

For compute resources, the hypervisor allows and provides APIs for number of VCPUs or VMs instances to be increased or decreased according to workload, or move VMs from one host to another. They also ensure isolation among VMs to minimize performance interference. VMs can also be pinned to specific VCPU. Xen hypervisors for instance allows users to control the fairness of the scheduler through resource caps, shares, etc. 

More information in the attached references.

http://ldc.usb.ve/~figueira/Cursos/ci4821/Material/Tema3/Articulo_Xen.pdf

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.485.9654&rep=rep1&type=pdf

https://en.wikipedia.org/wiki/Hypervisor

Conference Paper A Component Based Performance Comparison of Four Hypervisors

Ibidunmoye provided a great answer above, but I do have one minor quibble with his statement "Though memory is not really virtualized (not shared)...".  Memory is indeed virtualized.  Sharing is not the key point that determines whether something is virtualized. Rather, if the resource is managed by the VMM and allocated across the guest VMs, then that resource is virtualized. Management of a resource by the VMM is either by time-partitioning, such as time-slicing a CPU; or space-partitioning, such as by dividing the memory into smaller pages and giving (possibly exclusive) access to some of the pages to each guest.