How can I design a 2 BIT ADDER using AHDL

Altera is a company that makes FPGAs (field programmable gate arrays - esensially reporgrammable circuits). Quartus is nothing more than a compiler to get your code onto this chip.

Modelsim is a separate program by a sepearate company (mentor) that can be used to simulate code in its text form, but you cant do this with AHDL (because it's an old and dying proprietry language). Quartus does have a very basic simulator that lets you simulate compiled designs, but modelsim can do this too, and is much more powerful.

For any designs, all you will ever see is a signal trace - the skill is knowing what stimulus to give it. With modelsim you can design a testbench in VHDL that can produce all manners of stimulus.