The mechanics are usually simpler than people expect. Most networks put monthly products on a rechargeable smart card or their official app: buy the card at any metro station machine or ticket window, load the monthly pass, and tap in and out like everyone else. Increasingly you can skip the card entirely and buy through the operator's app with a foreign bank card, though some apps demand a local phone number, in which case the station machine remains the reliable route.
The benefits play out differently for locals and visitors. For residents the pass is a commuting no-brainer. For visitors the value hinges on trip volume: it wins if you ride multiple times daily for most of a month, and loses to weekly passes, tourist passes, or capped contactless fares for shorter stays. There is also a hidden benefit people underrate: with unlimited rides you stop rationing yourself, hop on a bus for two stops without thinking, and end up exploring more of the city.
Check zone coverage against where you are staying, whether suburban rail and airport lines are included, and calendar-month versus rolling validity. The operator's official site answers all of this in one page.