If you want to play the co-op campaign
If you want to play the whole campaign in co-op with your friend, then you must both be in the same point in the campaign mission, and after all your friends are in a Link Party, you can all start the mission together by interacting with the NPC at the same time. Now, whichever friend completes the cutscene and gets into a monster fight, the game will automatically send out the quest invitation to others and they can join the fight and also continue their part of the cutscene after the fight is over.
This method worked for me 100% of the time and it worked only as a Link Party. Environment Party kept kicking us out every time a cutscene started so it’s best to use this method.
If you want to play co-op for non-campaign stuff:
If you wish to share the same game world, then you have to send an invite using the Environment Link, which shows up in the Communications tab > Link Party section after you get in the Link Party with a friend.
Environment Link is best for hunting monsters together without affecting the campaign. If you wish to farm for resources with your buddy, then use the Environment Link.
If you want to play co-op everyday:
If you wish to share the same world and server without an Environment Link, then you must make a Squad and add your friends to the Squad and then join the Squad Lobby by going to Select Lobby > Squad Lobby when you boot up the game. This way you can see your friend in the same world as you without Environment Link and even do campaign quests without getting kicked out of the host friend’s world every time there’s a cutscene.
You can make a Squad after talking to the NPC outside the massive tent (ahead of the smithy) in base camp at Windward Plains.