DLC in Elder Scrolls Online can be obtained by purchasing it in the Crown Store. All DLCs in the game are free to access for players who have a current subscription (ESO plus) to the game, however if the subscription ends or lapses access is lost until it is renewed.
Important information for console players: All DLCs, including Morrowind, are bound to one single account they were purchased on, and do not come included in the "Gold Edition" or "Morrowind Edition" disc copies of the game. If you buy a physical copy, you will get a code for the DLC content that will not be available to other accounts on your same console unless they buy the content too.
DLC is paired with large free updates that make changes to the core game. You can find them in the Patch Notes page.