Our in-client chat room is the primary place for match organizing.
If you want to play a Factions match, I suggest joining the Factions chat and setting it to auto-join by clicking the gear icon in the upper-right corner of the chat window and checking that box.
Be on the lookout for chat posts from people in the process of organizing a match, and for random custom game invites.
It wouldn’t hurt to add some Factions Summoners to your friends list, either.
It also helps a lot if you can join your faction’s chat. For example, if you’re Ionian, join the IONIA chat; if you’re Bandle City, join the BANDLE CITY chat.
Why does this help? Well, put yourself in the shoes of someone organizing a match. It’s not obvious which people in the main chat are in one of the two factions involved in the match you’re setting up. But if you need, say, Ionians, it’s easy to hop into the Ionia chat and invite those people.