The online PvP portion of Armored Core 6 doesn't unlock until the start of Chapter 3. This represents roughly 10 hours of playtime. Once you get there, the Nest option in the Garage will unlock and you can head online for some multiplayer battles.
In this menu, you can select Custom Match and then choose to create your own Room or join someone else's. You can then compete in either 1v1 or 3v3 encounters to see who's the better mech pilot over three rounds. There aren't any rewards to be gained; this is just a simple battle against opponents.