Kabul is too big to walk between districts and not designed for tourists to navigate alone. The practical option is to hire a car and driver for the day — every hotel and tour operator can arrange one, and a trusted driver is by far the most useful thing you can have in Kabul.
Taxis are yellow-and-white and metred only sometimes; agree the fare before you get in. Shared minibuses run fixed routes for a few cents but are unmarked in Persian script and impossible to use without local help. Walking inside an individual neighbourhood — Murad Khani, Babur's Gardens, the old bazaar — is fine in daylight; walking between districts is not.
Carry your passport, dress conservatively, and follow your guide's instructions on which areas to avoid on any given day. The Taliban's security checkpoints are part of the basic infrastructure of moving around the city.