The most convenient form of travelling around Karachi is by taxis.
Yellow cabs are quite popular, and can be found almost anywhere around the city. All you have to do is stand on a main road and wait for one to appear. Their fares are reasonable (around Rs 10 per km). However, due to constantly varying petrol and gas prices, taxi drivers do not usually use their meters - if they have one installed, that is. It is therefore advisable to let the driver know the exact location of where you want to go, and then fix the fare with him before getting in. You might consider letting several high-fared taxis go before deciding to take one that you find cheaper.
Black-and-yellow taxis are like the 'big' buses of Karachi. They have a slighlty larger seating and luggage carrying capacity, and considerably lower fares. They can easily be found on most of the roads of the city.
Autorickshaws are much cheaper, but much more noisy, and seat two, or at most three people. As they are much smaller than regular cars, their drivers can easily steer them out of traffic jams, and often take shortcuts through narrow sidestreets and lanes.
Some private companies provide a much safer and comfortable way of travelling in the form of Metro Cabs. These are elegant, air-conditioned cars, and can be called to pick you up from any location. The fare is consequently higher, around Rs 15-20 per km, plus a varying calling charge. Within Karachi, you can call for their services at 111-222-787.