Playing multiplayer with other people (whether friends or strangers) is a great way to enhance the game or make it more challenging.
While players don't need to have the same DLC, all players must have the same mods enabled (or lack thereof), or else you will not be able to join each other's games.
Types of Multiplayer
LAN
In the Multiplayer menu, this is the default. CKII will scan for player-hosted games on the Local Area Network. The computers of the players must be physically connected somehow, or a simulated LAN can be established with a program such as Tunngle, Evolve or Hamachi.
Internet Game
Host
First, the host has to portfoward the following ports : "2300-2400 (UDP and TCP), 47624 (TCP only) and 1630-1641 (UDP and TCP)". In some cases Windows firewall can block the connection, shutting it down or opening the ports in it is advised.
Then, you get in the multiplayer menu and click "Host", then choose the session's name, password, tag and description. You select the starting date and/or the save to load then you press "Host" again. Now you can select your character and wait for your friends.
Other players
In order for them to connect, they must click the "refresh internet" button (If this button is invisible, they must register their game in the Paradox Interactive official website and wait about one day before getting it) and select your server in the list. They will automatically connect to it. Now. they can choose their character and press the "Ready" button. When everybody's ready, the host can finally start the game.
Mechanics
When the players first join the game, they download the save (if there is one) from the host. Then they choose their characters and signal readiness. The host server performs another check when all players enter the game after the host has begun. Thereafter, the host controls the speed (though any player may pause the game by clicking the date. Note that the space bar will not pause the game in Multiplayer). If the speed the host has selected is too fast for players, the host server will automatically lower the speed to allow the slowest player to remain in sync.
The game will automatically pause if a player disconnects or becomes out of sync. It is advisable to save the game any time either of these happens.
Because checksums change each time a player resigns from a game, it is often the case that all players involved will have to restart the entire CKII game in order to regain the same checksum they were playing on.
It is advised to use 2X faster as minimum speed to avoid desyncronization between players.
DLC Compatibility
So long as all players have the same game version, there should be no issues. The game will play as though everyone in the game has the same DLCs as the host.