General summoning is only done by witches, the Mage's Guild, and at temples.
Only a single NPC in any given coven, mage's guild or temple can do a summoning.
If a daedra summoning is selected in a witch's coven, randomly select which daedra is being summoned that evening (exclude Hircine, who is only summoned by the Glenmoril Wyrd Witches). If this is Glenmoril Wyrd, they'll only summon Hircine.

witches summoning price = 100,000 + ((100- pc reputation)*1000)
chance appearing = (30* + pc reputation + special day) max 95%
5% chance to get Sheogorath on any given summon
special day adds 30% chance to summon that daedra

Can only get a quest from each daedra once, otherwise will be punished by a monster.

Best chance to get a good summoning is to go through the Mage's Guild or temple, unless you want Hircine.