How long does it generally take from the time a baby starts teething to the time she cuts a tooth?

Variable! No definitive timing as baby's teething can be long and drawn out or episodic. Some infants are indifferent with tooth erruption/teething. Bottom front teeth followed by the top front are seen errupting average 4-6 months of age. Of course there are always early and late variations to this.
Get a lottery ticket. You have asked a question that really no one can give a solid answer to. Teeth (baby and permanent) erupt at their own speed. And that speed can vary even in the same persons mouth. Be patient, sympathetic for your child and you can help by getting a cold teething toy for the child or some numbing agent to place on their gums and for yourself, grab a glass of wine. Soon it'll pass.
A couple weeks. It really should not take long before they start to cut, however there may be multiple teeth cutting not on the same schedule. I rec you use teething rings or something firm and chewy to help aid the process. Infant pain relieves can help a bit if needed. Often cold chewy is comforting for the child, but all kids are different. Good luck.