Malaysian Airline System (MAS) is the main domestic airline, servicing both the peninsula and Sabah and Sarawak. Fares are reasonable but it's unlikely that you'll need to fly in Peninsula Malaysia unless you're in a real hurry. It's cheaper to fly to East Malaysia from Johor Bahru than from KL. In East Malaysia, flying is often the only quick way to get around. Note that flights in East Malaysia are frequently fully booked during school holidays and are prone to delays due to the vagaries of the weather.
Peninsula Malaysia has a fast, economical and widespread bus system, and this is generally the best way to get around. Sabah has excellent roads, and minibuses ply the main routes. Buses ply Sarawak's major trunk road, but hardly anywhere else. Peninsula Malaysia has a comfortable and sensibly priced railway system, but there are basically only two lines: one linking Singapore to Thailand via KL and Butterworth, and the other branching off this at Gemas and heading north-east to Kota Bharu. In Sabah, there's a narrow-gauge line through the Pegas River gorge from Tenom to Kota Kinabalu which is well worth catching.
In Peninsula Malaysia, long-distance taxis are twice the price of buses but they're a comparatively luxurious and efficient way to travel. If you want to get around by car, all major car-rental firms have KL offices. There are no boat services between Peninsula and East Malaysia, but fast boats ply the rivers of both Sabah and Sarawak.
Local taxis in Malaysia are metered. Rickshaws have all but disappeared in KL, but they are still a viable form of local transport in provincial areas. KL has a notoriously bad public transport system, and peak-hour travel in the city should be avoided at all cost.