You are confused.
First, RAM is not used (directly) by processes. It is the operating system kernel which manages RAM and provide virtual address spaces to processes thru virtual memory (so your program, running in a process, has its virtual address space). Read a good textbook like Operating Systems: Three Easy Pieces to understand these concepts.
There is no way to share RAM across network, and that would make no sense (because the bandwidth and latency of RAM is a lot better than that of network). Relative to the speed of RAM, the network is many thousands times slower (so is always a bottleneck) !
You might design your software as some distributed computing using message passing between processes running on several hosts.
You have a lot to learn; look into MapReduce, MPI, sockets, 0mq etc etc....
You probably want to use Linux or POSIX (because it is dominant in distributed or cloud computing). Read some Linux programming book like ALP or something newer, then see syscalls(2) and the many man
pages they refer to. Notice that socket(2), poll(2), socket(7), tcp(7) (and other system calls) are highly relevant to your needs.
You might want to use some database. Perhaps RDBMS, PostGreSQL, MongoDB, REDIS or even memcached might be useful.
You need to learn and read a lot of things before coding.