I made a video below, here's the text version as well:
Warning: the AC4 matchmaking/party system is literally the worst I've ever seen in my entire life. A convoluted process with constant bugs. Between the AC4 "party" and the XB1 "party" it will often confuse where you are, or if you're even there at all. Sometimes this will cause it to crash, sometimes it won't, so it may still look like you're connected when you're not. So remember to hold down your Xbox power button for 5 seconds to hard reboot it, or unplugging it for 10 seconds is even better (yes, it makes a difference). Remember that trick, you're going to need it.
So here's a guide on how to actually match up! (clan v clan method, definitely the best)
1) Start/join a clan.
Once you're into the multiplayer section hit RB once to get to "Abstergo Network" tab (group of 3 people icon). Go down to "Clan" and start a clan, then go to "invite friends". To invite someone to your clan they must be on your friends list and they must have played at least 1 multiplayer game already.
2) Two separate clans, two separate Xbox Live parties.
We'll come back to this, but if you go back to the center (Abstergo icon) and go to "Custom Match", choose "Adversarial", "Clan", and "Domination". Notice the 3 panes, and the top right one that has the spaces for 8 player icons (with 4 blocked out) - this is the first level of the AC4 party system. The only icons you want there are those in your clan. The game will often automatically put players here and refuse to drop them, even after a soft restart, so do a hard reboot if you need to. If non-clan members are there they'll have a red ring around their icon and you won't be able to start. So get each clan into their own Xbox Live party, then into their own AC4 party where all their icons show at the top.
3) AC4 party stage 2, Player List game lobby
Below "Mode Preference" where you chose "Domination" should now be blue and say "Play with party", hit it and you'll be in what looks like a game lobby. This should have automatically sent an invite to anyone in your AC4 party: it will tell YOU that invites were sent, THEY can accept by pressing RB once to go to the "Abstergo Network" tab again and go to the new 5th row on the bottom that says "invites" or something. Once they accept that YOU will receive an Xbox message saying they were added to the game, and they should show up shortly on the player list below your name. If none of that happened then back out and hit the blue "Play with party" button again to try and get it to send an invite. If that still doesn't work then both of you have to hard reboot and start over. Isn't this great?
4) Hit X to play with party, and cross your fingers
If you made it to the Player List/Lobby you'll see a prompt below that says to press X to play with party. This is where both clans/parties will want to do it at the same time so you'll match up. Then hope you find each other. Then hope it doesn't drop the other team, if it even NOTICES that it dropped the other team. If something doesn't work you can try going back to step 3 but if something's funky just hard reboot. Again.
5) You're in the game!
One achievement per person per game, have that person defend a point, get on a roof so you're easy to spot, and have the other team just keep running to you. Once the bar goes fully red or white it's game over. Press A to skip the results screens, vote on a map, and hit ready. Do all that and you won't have to wait out the clock between matches.
Congrats, that may be the hardest achievement you've ever received!