hey please suggest me, the proper connection and method to control simple dc gear motor via potentiometer using arduino and to change its polarity also while speeding up or speeding down :~
To change the polarity you need an h-bridge. To change speed you just PWM one of the motor power lines, or (depending on the h-bridge) PWM the bridge's enable pin.
Have a look here for instance, although there are newer more efficient chips than that L293. Principle is still valid, though.
edit... sorry should clarify: you PWM the motor based on the reading from the pot. Have a look here for PWM.