When to go: You can visit Kuala Lumpur at just about any time of year. Weather-wise, the months of June to August are the driest, but due to its location near the equator afternoon thunderstorms are a possibility at any time. The city is at its most crowded, with correspondingly expensive hotel rates, during the Formula One races in early April.
How long to stay: Three days should be enough time to take in the sights of Kuala Lumpur. On a longer stay, you can consider day trips to places that are futher afield, such as Melaka - although I would strongly recommend that you spend at least a couple nights in Melaka.
Where to sleep: The city is rather spread out, so there is not necessarily any ideal area to stay in. Hotels in the Bukit Bintang, KLCC or Golden Triangle area will put close to a lot of dining and shopping options.
Getting around: Kuala Lumpur is a rather spread out city, so you won't be able to get most place on foot. Taxis are cheap and plentiful, although sometimes it takes a bit of negotiation to get them to take you where you want to go and use the meter. Most, but not all, tourist attractions are close to one of the many trains (and monorail) that cross the city. Note that most of the lines don't have consolidated ticket, so some trips may involve buying a ticket to one destination, where you'll have to buy another ticket for another train to your final stop. The trains, along with the Hop-On Hop-Off tourist bus service, can get you just about anywhere you want to go.
What to see: For many, the Petronas Towers are a must-see. Be sure to get there early in the morning (8:30 am) to book a ticket up to the skybridge. A walk around the Merdeka Square area will be of special interest for those interested in architecture, especially of the colonial era. Then there's the shopping. I tend to think the shopping in Kuala Lumpur's Bukit Bintang area out-does some of the more well-known shopping destinations like Singapore or Bangkok, especially for cameras and consumer electronics.