Core gameplay is running pve missions against hordes of enemies with various objectives. Most can be played either solo, on your device or in co-op with up to four players, with one player hosting and the other three connecting to them.
Each Warframe (class) has four abilities, a passive, and their own stat distribution. You cast abilities using energy you pick up from dead enemies, and various other sources. You go into each mission with a primary ranged weapon, a sidearm and a melee weapon, along with other types of equipment you unlock as you progress through the story.
Warframes and equipment are all upgradeable via Mods, which usually will multiply the base stats of whatever they’re equipped onto, but can also do things like modify how abilities work or add unique buffs. The amount of mods you can equip on something is determined by its level, which you increase by using it.
You have an account level called Mastery Rank which you increase by leveling up (mastering) equipment for the first time. You don’t need to keep equipment after mastering it but some of it can be hard to attain and there’s a lot of reasons you probably should.
You’re limited on the number of equipment you own by the amount of slots you have for them, which are primarily increases by buying them with platinum, the premium currency. Thankfully you can trade that currency with other players and the slots are extremely cheap.
There’s a lot I’m leaving out and certainly things I’m forgetting but that’s mostly the gist of it. The wiki is extremely robust if you want to know anything else and they somewhat recently started hosting it themselves at wiki.warframe.com so you don’t have to deal with fandom.