Let's take a look at how to get to him, his abilities, and some simple strategy to defeat him.
Before You Go
Get the quest "Chamber of Secrets" from an Argent Dawn Emissary. There's one in Light's Hope Chapel in Eastern Plague Lands, and there are a couple in the capital cities. This quest can be shared with other raid members. After you've defeated Tenris you can pick up the quest item from his room to complete quest. Return the quest to either Light's Hope Chapel or the NPC you picked it up from.
How To Reach Tenris Mirkblood
Go into Karazhan and clear up to Attumen. Go up the stairs in the back of Attumen's room, right around where the repair guy is. You'll have to clear several sets of mobs. If you are in T5 gear or below, take your time. Most mobs are grouped up in packs of three to five. There are also a few roaming packs that you'll need to watch out for.
At the top of the stairs you can go right or left. While both will eventually take you to Tenris, going right is the quickest. Clear the rest of the mobs until you come to Mirkblood's door. Be sure to clear any mobs around the area that might be patting back and forth.
Do not open it until you are buffed up and ready to face him.