It doesn't directly access memory. The addresses in your userspace program are not the actual addresses of memory in the ram sticks - there is a table of mappings that the kernel sets up. When your process asks the kernel for memory, it says "i need 5KB, please put that at address XYZ". The kerenel goes and finds 5KB unused, probably at some other address ABC, and creates a mapping in the table that says XYZ translates to ABC. Then the kernel sets the MMU of the CPU to use the table for your process, and switches back to unpriveleged mode, letting your process run again. Your process in unpriveleged mode sends an instruction to write to the memory at XYZ, but the cpu will translate that instruction to ABC and write there instead.
VMs (well not emulated vms, but if you're doing an x86 vm on x86 or an arm vm on arm) do something similar - an inaccurate (but useful for the concept) way to think of it is that the cpu does 2 layers of MMU for user processes in a vm.
The kernel code isn't running directly when your program accesses memory, but it sets up the cpu so that the kernel still has control over your memory, and you only have access to what the kernel allows - its mediated by the kernel.
