@ tarun 
ideally speaking there is no shrtcut for pulley problem technique . 
but u can infer from the following points . 
i am giving you some tricks to solve the problems in laws of motion kindly follow that 
1- always draw fbd of individual bodies given in the system , (blocks , pulley etc ) 
2- when u have to show direction of tension forces in contact with fbd of a body then always use the concept – TENSION ALWAYS ACT AWAY FROM BODY . 
3- MAKE THE RIGHT SENSE IN YOUR MIND THAT IN WHAT DIRECTION THE BODY WILL MOVE 
4- NOW MAKE EQUATION ACC TO MOTION OF BODY 
trick – for making equation in the fbd , always take those contact forces as +ve sign which are along the sense of motion , and take those as -ve which are opposite to the sense of motion , 
imp points 
1- spring balance read the tension in the string 
2- if string is inextensible and all pulley are fixed , then magnitude of all masses connected through string is same . 
3- in case of movable pulley , the acceleration of all masses are diffrent , in order to get relation between their acceleration we use the TENSION TRICK . 
TENSION TRICKS ARE A THE VERY SHORT WAY TO APPROACH THE PROBLEMS , but remember concept of movable pulley are very imp . for jee advanced and mains exam . 
SO, PRACTICE FEW QUESTIONS FROM D C PANDEY MECHANICS BOOK AND TAKE H C VERMA FOR CONCEPT , U WILL GET FAMILIER WITH IT AUTOMETICALLY 
ALL THE BEST ..