Nanny Ogg has a talent for getting along with people and fitting in. As described in Maskerade, people, after knowing her for fifteen minutes, feel like they have known her all of their lives. Granny Weatherwax knows about this ability, and recognizes its use, and wonders sometimes if it would have been worth acquiring it.
Contrary to Granny Weatherwax, and indeed the stereotype of witches in general, Nanny Ogg doesn't live in an isolated, crumbly rural cottage but in an expansive and well-looked after town house in the capital of Lancre, called Tir Nani Ogg ("Nanny Ogg's place," and a pun on the Gaelic name for the Land of the Ever-Young). She fills it with knick-knacks such as pink skulls and rude garden gnomes that serve no useful purpose except to highlight her eccentricities. She shares this home with Greebo, a tomcat of evil aroma and astonishing viciousness, whom she can see only as a fuzzy harmless kitten.
In The Art of Discworld, Pratchett says, "I've always suspected that Nanny is, deep down, the most powerful of the witches and part of her charm lies in the way she prevents people from finding this out." In his short story "The Sea and Little Fishes" Nanny Ogg also identifies herself, and the Ogg family as a whole, as having immense natural magical talent, but as less willing to work it as hard as Weatherwaxes do.
It should also be noted that Nanny really likes to eat and drink despite only having one remaining tooth (The sight of Nanny Ogg eating a pickled onion supposedly brings tears to the eyes). When she's drunk she has a tendency to sing very "special" songs, the most popular being "The Hedgehog Can Never Be Buggered At All" or simply "The Hedgehog Song" (never really unveiled by the author beyond a few lines, but many readers have written their own versions ). "The Hedgehog Song" was probably borrowed from a Harry "Haywire Mac" McClintok song recorded in 1950 by Cook Records and American Folkways (available on iTunes oddly enough). A close runner up for the most popular Nanny Ogg song is "A Wizard's Staff has a Knob on the End", a version of which has been written by Heather Wood, with music by Dave Greenslade
Nanny Ogg's bath night, as described in the novel Lords and Ladies, is an event feared by the entire population of Lancre, chiefly because she sings any and all of the above songs, accompanied by banjo, whilst bathing, and the tin bath amplifies her already overpowering vocal presence such that the audience is not so much "captive" as "hunted down". Residents of Lancre tend to hide their livestock at this time as well, as the trauma causes the sheep and goats to "give yoghurt for weeks" afterwards. This event usually occurs once a year, so everyone has plenty of time to prepare.
Nanny Ogg embarrasses Tiffany by talking about Roland, Tiffany's nervous pen-pal, and other romantic prospects. Nanny Ogg is very funny and has a tremendous laugh that, as Terry Pratchett put it, "could even have embarrassed the little, wooden man".
In the Discworld amongst the duties of a witch are midwifery and laying out the dead. If possible, people call Nanny for the former and Granny for the latter. In effect Nanny and Granny make a perfect team with Granny doing what needs to be done and Nanny bandaging the wounded. Indeed, in Thief of Time, Nanny Ogg is sought through various timeframes as she is/will become the best midwife in the world.
She has an ambiguous relationship with Count Casanunda, whom she met in Genua. Nanny Ogg is also the muse and center of Leonard of Quirm's masterpiece, the Mona Ogg: her teeth follow you around the room, they say. She briefly took on Tiffany Aching as an apprentice after the death of her previous mentor, Miss Treason.
It was observed in more than one occasion, by Granny Weatherwax, that Nanny Ogg has impressive social skills. She has demonstrated the ability to socialize with all kinds of people within a very little time (Maskerade, Witches Abroad, Lords and ladies) which sometimes leaves Granny wondering 'if Gytha has some sort of special magic'.