If any player does not own the game, the game will be limited to three people total, only the first island scenario, and always the same exact map - resources always in the same place and with the same number values.
If everyone owns the game, the maximum players is four (six with the next update), other scenarios are available, and the map can be randomized - resources and numbers will be in different places.
To invite players to a game they need to be on your friends list. Click on your avatar, select "Friends" and then "Add a Friend". In the search window enter your friend's username exactly as they spell it. Once you find them you can send them a "friend request". After they accept you will be able to start a custom match and invite them to play with you.