Rosabeth of Melfia is a petrified pyromancer woman who stands in front of a lever on the path to the Shaded Woods. You will need to unpetrify her with a Fragrant Branch of Yore.
Fragrant Branch of Yore locations:
A Fragrant Branch of Yore can be purchased from Merchant Hag Melentia in Majula for 12000 souls. Alternatively, there are other locations where you can find them if you do not want to spend the souls: at the beginning of Black Gulch after dropping through some corrosive urns, and there is one in the chest after the Lost Sinner.
To get a free Fragrant Branch of Yore early on go to No Man's Wharf, go down from where you ring the bell, and underneath that platform is a stone building (you should be attacked by a couple of fast ninja guys) Enter the building, there will be a couple of enemies and poison pots. In the far right corner from the door is a chest, this has the branch in it. Also hit the wall next to the chest, it breaks. Thanks to SK Diabolic for this location.
Start at the bonfire where the eagle drops you off after you beat the Pursuer and hitched a ride (The Tower Apart). Leave the tower and follow the route into the building which contains all the dogs and exploding kegs. Exit this building through the door on the bottom level and you'll be on a flat platform that stretches between buildings. There is a chest in the back corner of this platform that contains (among other things) a fragrant branch of yore. And watch your back as you go for the chest, these new enemy placements are fantastic. Thanks to Catatonic Nali for this location
Rosabeth's Location:
To get to her, go down the path past some rocks from the exit of Things Betwixt (toward Majula), but turn off the path to the left a bit before the archway. there is a cave entrance. Follow this and you should see Benhart of Jugo sitting on the ground, continue inside to find petrified Rosabeth in front of the lever.
Once she is unpetrified talk to her until you get the option to give her equipment. Then simply give her any clothing you want her to wear, be warned: you will not be able to get the equipment back so don't give up anything you need/want.