Requirement 1: defeat Starscourge Radahn
Radahn is fought at Redmane Castle in Caelid during the Radahn Festival. Talk to Blaidd or Ranni, or simply reach the Altus Plateau, to start the festival. Take the waygate inside the castle to Wailing Dunes. Caelid region page.
Requirement 2: defeat Mohg, Lord of Blood
Mohg is at the far end of Mohgwyn Palace. The two ways in are White Mask Varré's questline (which gives the Pureblood Knight's Medal, usable from Limgrave) or the Sending Gate hidden behind a Sanguine Noble in the western Consecrated Snowfield. Mohgwyn Palace region page.
Enter the Land of Shadow
After Mohg falls, walk to the giant cocoon behind his arena and interact with the withered arm of Miquella. You arrive at the Gravesite Plain, where the DLC begins. You can return to the Lands Between at any time via fast travel.
Level check
The publisher recommends level 150 with a +25 weapon. Practically, level 120 to 150 is fine if you collect Scadutree Fragments immediately. Use the DLC map with only the Scadutree filter enabled.
Related questions
Do I need to beat the base game first?
No. You only need Radahn and Mohg defeated. You can enter the DLC before Leyndell if you are strong enough.
Does entering the DLC affect NPC quests?
No base game quest is failed by entering the Land of Shadow, but time-sensitive DLC quests do advance as you defeat DLC bosses, so talk to every NPC at the Three-Path Cross early.