1) To use a module (implementation) not an instance (module loaded somewhere of the process using require) in different process, you only need to require that module wherever you need.
If you run two process, for example, process A that use 'MyModule' and process B that use 'GrabModule', but you only need that 'GrabModule', in process B, can access to the exported properties of 'MyModule' then you only need to use require('path to MyModule').
2) On the other hand, if you need that a process B, can access to a module's state (a module that has been executed, because you use require in somewhere) of a process A, then you need to use a IPC (Inter-process communication) that allows to exchange data between process A and process B, and build or use the same protocol in both, over it.
Depending if your process are in the same machine or in different one, to can use some IPC build in the same OS, as nodejs offer with child fork (http://nodejs.org/api/child_process.html#child_process_child_process_fork_modulepath_args_options) or use an IPC built in some network channel.
For example, you can use the publish/subscribe messaging system of Redis (http://redis.io/topics/pubsub)