Tribhuvan airport is east of the city, and you can get a taxi to Thamel for a fixed fare.
The best way to see Kathmandu and the valley is to walk or ride a bike. Bus travel around the city is very cheap but unbelievably crowded, so much so that you'll probably miss your stop because there's no way you'll be able to see out the window. Tempos (like giant auto-rickshaws) follow similar routes for similar prices. A dilapidated trolley bus runs from near the National Stadium to Bhaktapur.
Taxis are reasonably priced, and drivers will use their meters if pushed. Around Thamel and other tourist hotspots, you may have to bargain for a (usually elevated) fare before you set off. Moving cabs are more likely to use the meter than stationary cabs outside tourist sights. Auto-rickshaws cost about half as much as cabs, though once again, you'll have to negotiate a price. Bicycle rickshaws are really a novelty these days - fares are often more expensive than cabs but you will get a unique viewpoint of the city.
You can't rent cars to drive yourself, but you can rent a car with a driver - a day trip around the valley will cost you about USD$ 50.00 plus fuel. There are motorbikes for hire around Freak St and Thamel, but the congestion is crazy and you'll spend much of your time stuck in traffic breathing in truck fumes.