How many downlights should I install ? Or how many downlights do I need ?

This is a difficult question as their are many factors that need to taken into consideration:

What type of room are they are being fitted in ? Lighting standards state that different rooms require different lux levels. For example Kitchens should be between 150-300 lux, living rooms should be between 100-300 lux,  bathrooms should be about 150 lux and living rooms should be

Personal choice, how bright do you actually want it to be ?

Will the downlights be dimmable ? If they are dimmable then you can have plenty of bright downlights as they can be easily dimmed to your  your mood / room function.

• What type of lamps are being fitted in the downlights ? Most low energy lamps such as LED and CFL are not dimmable.
• Beam angle of chosen light source? Lamps have different beam angles. Beam angles describe how the light is spread out. For example a 50W halogen lamp could have a narrow beam angle of 25 degrees or a 50W halogen lamp could have a very wide beam angle of 50 degrees. Both are 50W but the light would be used differently and impact on how many downlights would be needed particularly in a larger room.

As a general guide line, based on using 50W halogen downlights, the downlights should be fitted between 500mm and 600mm away from the wall. For kitchens they should be fitted the same distance away from the cupboards or you will be illuminating the top of the cupboards and wasting light. The downlights should then be separated by gaps of 900mm to 1200mm. Approximately one downlight per square metre.
For example, a kitchen with a working area of 9 metres square ( 3 x 3 metres )  ie not including cupboards etc would have 9x 50W downlights and provide an adequate lighting ambience. 

What I would recommend is choosing the lamp / downlight that you like. Ordering one on a sale or return basis, wiring it in to a plug with enough cable to hold it up to your ceiling. This will give you the best idea of the brightness and beam angle.