To play with friends in New World, you must first make sure you are both playing in the same region and game world. If you are not both in the same region and game world, you will not be able to invite or join each other's group.
So, for example, if you are in US East and your friend US West, you will not be able to invite your friend to join your game/group vise versa. However, if you are in US East but in a different game world than them, you still can't invite them to your group/game.
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So you will need to pick the same region and world. Once you do this, you will be able to play with friends by first adding them in the game. To add your friends, hit m to open the map menu and then hit the company as shown below.
Under the company menu, you will have an online and group option, and you can use the online option to add your friends and then use the group option to add them to your group.
Clicking the online button will open up a tab, and if you want to add your friend, just type their name in and send them an invite. Once they accept, you will be able to invite them to your group using the group option from before, and that will be how you can add your friends and play with them in New World.
Check out some of our other guides for New World!