Frame Fighter is a mini-game in Warframe where two players can fight each other in a beat-em-up style game. To get access to Frame Fighter, you will need to purchase the Ludoplex from Cephalon Simaris. This will cost you 50000 Standing.
You can earn Standing with Cephalon Simaris by finished daily bounty challenges. To get these, you need to visit Cephalon Simaris on any Relay, and he will give you a synthesis target to track down and scan.
When you purchase the Ludoplex from Cephalon Simaris, you then need to place it in the Orbiter as a decoration. Open your main menu, then go to the Equipment, Orbiter, and choose the option to decorate the Orbiter. Find the Ludoplex and then place it where you like in your Orbiter. Interact with the device and select Frame Fighter from the options.
Now, for the Nightwave challenge, all you need to do is load into the game. If you wish, you can set yourself to solo, load into the game, and abort the mission, and the challenge will be automatically complete. If you do want to play against another player, just leave your matchmaking on public.
When you purchase the Ludoplex, you will be able to play Frame Fighter and will have access to default characters, but other characters will need to be found in the world. Frame Fighter fragments are hidden through various levels, and scanning them will give you access to the Warframe in the mini-game.
FIghts will play out similar to the Street Fighter games that the mode riffs on, so for PC players, it is worth using a controller for ease of character control.