The Resistance is a military organization and consequently follows a military chain of command. The commanding officer is General Leia Organa.
The Resistance appears to be a small, commando-style organization aimed at preventing the expansion of the First Order via precision strikes on critical targets. It seems to rely on small numbers of highly trained and well-equipped units to make hit-and-run attacks and counterstrikes. In the event of a large-scale engagement, they would call for help from the Republic navy.
The Resistance does not control any sovereign territory, being a subsidiary organization of the Republic. They have one known planetary base, although there may be others.
The Resistance has access to the formidable technology of the Star Wars galaxy, but it does not appear to have the resources of a large army or navy. They have the ability to engage in precision military operations, but they do not appear to have the resources to win an all-out war with the First Order.