Given a person got a spare computer or few with some RAM (e.g. 16GB), how can you make gains (e.g. tokens) from just running EOSIO decentralized operating system with some minimal effort? What is the general approach?
EOSIO doesn't have mining since it's not a proof-of-work system. It has block producers instead. Running a block producer on the main chain isn't a turn-on-and-forget type job, or a use-a-spare-machine type job. It's more like running a mini data center, with multiple high-end machines performing dedicated functions backed by redundant network connections. Several block producer candidates are new companies employing multiple full-time people, backed by VCs.
While you can't earn just by running a node, you can earn from leasing EOS tokens that you already own via leasing market applications such as Chintai. See their website https://eos.chintai.io
The current expectation is that a "good enough" Block Producer will host 10 servers and provide 4 public endpoints, and earn something more than 100 new EOS tokens per day, depending on whether they are Active or Standby, and how many votes they receive.
A pretty good FAQ is here: https://medium.com/@bensig/eos-block-producer-faq-8ba0299c2896