Dealing with the Telvanni can be as easy of difficult as you choose to make it. Your first stop should be Master Aryon in Tel Vos. He will immediately agree to naming you Hortator and point out that you will have a difficult time with Archmagister Gothren and probably have to kill him (which, he freely admits, would be doing him a great favor). Now it's time to get the rest of the councilors on board.
Mistress Dratha (Upper Tower, Tel Mora) is the closest to Tel Vos. If you are female, she's in your pocket. If you are male and a member of Telvanni, get her disposition up to 80 and she's yours. If you are a male and NOT a member of House Telvanni, you'll probably have to take her out (and I don't mean "to a nice restaurant") because it's doubtful that you can get her disposition up that high - she hates men.
Master Neloth (Tel Naga in Sadrith Mora) will name you Hortator if you can get his disposition up to 70 or more. Otherwise, take him out.
Mistress Therana (Upper Tower of Tel Branora) is a piece of cake if you catch her in the right mood. You'll need to get her disposition up to 30 and tell her some nice stories (requires a Speechcraft of at least 30).
If you are a member of House Telvanni and have got a few ranks under you, you'll have to deal with Master Baladas (Arvs-Drelen in Gnisis). If you are not a member of Telvanni, then he is not a councilor and you don't need to mess with him. Convincing Baladas requires getting his disposition up to at least 30, but that chore should already be done.
Archmagister Gothren, on the other hand, will have to be taken down. Hard. And it won't be easy unless you go prepared. You'll find him in the Upper Tower in Tel Aruhn, flanked by his two Dremora bodyguards.
My solution was to use dialogue to force a fight. As soon as he started casting, I stabbed him with a custom-made Wakisashi that paralyzed on a successful hit. Then I killed him as quickly as possible and backed out to take on the two Dremora with a bit more room. In and out in a couple of minutes, no fuss, no muss and only a few minor wounds to mark the occasion (now you understand why I like Short Blades -- speed).
If you don't have the luxury of such a weapon, be prepared for one big fight. Gothren has a nifty little spell that isn't available anywhere else:
It's a touch-ranged spell, but it only has a base casting cost of 23 points and Gothren has 200 points to play with, plus 9 exclusive Restore Magica potions. If you don't take him down quickly, you're toast. The Dremora are there to keep you occupied while Gothren fries you with magic. Good luck.
Once Gothren is out of the way and the other councilors are either in your pocket or sleeping with the fishes, go back to Aryon to be named Telvanni Hortator.