Hamid Karzai International Airport sits on the north edge of the city, ten minutes by car from the centre. International flights are now limited and routed mostly through Dubai, Istanbul, and Islamabad, on a handful of carriers including Kam Air, Ariana Afghan, Emirates, and FlyDubai. Visa requirements are unpredictable and change frequently — confirm with the Afghan embassy of a friendly country shortly before you travel.
The overland routes from Pakistan (via Torkham), Tajikistan (via the Sher Khan Bandar bridge), and Iran (via Islam Qala) are open but the journey is long and security en route is variable. Almost all foreign visitors today arrive by air through Dubai or Islamabad on an organised tour.
Outside Kabul, internal flights connect to Mazar-i-Sharif, Herat, and Kandahar, and a couple of long-distance buses leave Kabul daily for the major cities. Road travel through the countryside is a separate question of risk and logistics; in practice tour operators do the planning.