The ability to group with other players is unlocked after completing the "Okki Island" quest line.
In order to invite a player near you to your group, target him or her and press "G" (this also allows you to use emotes). If the player is in a different location, you can open the chat panel by pressing "Y", type the name of the player you are looking for in the search box, and right click on his name to invite him.
Please note that the game distributes players by channels, so you may not see your party members initially. After a teleportation of any kind (for example to a new adventure), all players of your group will reach the same channel.