Hi Alvin,
I don't know exactly what kind of calculator project you are doing. Here are soem hints & suggestions.
You will need a microcontroller, LCD display, keypad & other auxillary circuitary such as power supply battery, power supervisory, etc.
1. Microcontroller :
a) I would suggest you to use a micro with ISP [ In system programming ] so that hurdles and troubles of programmer are avoided. consider using P89C51Rx2, AT89S5x etc.
b) Micro selection also depends and the kind of calculator you want to make for plain or general simple scientific calculator you can use any low-end 8051. For programmable high end calculators which can do complicated equations can plot graphs etc. consider using a micro with in built floating point unit.

2. LCD : You can choose to have wither a numeric, alpha numeric, or graphical display depending on kind of calculator you want to make.

3. Keypad : Use a matrix keyboard with the desired number of keys. Again the number of keys would depend on type of calculator you want to make.

Once your hardware is ready write the software and test it. I would suggest to use "C" rather than Assemby as you will be able to complete coding faster and easily. You can use Keil, SDCC etc.

Regards,
Prahlad Purohit