First of all, you have to move the chain of your bicycle to its largest front and the smallest rear cog. The rear derailleur will go too far from the chain, but you don’t have to worry about it. Then, you have to provide full slack to your derailleur cable which you can do by shifting its position.
After that, loosen the bolt of the cable anchor which is given beneath the rear derailleur. You will require a five millimetre Allen wrench to open the bolt.
Now, see the alignment of the smallest cog with the upper derailleur pulley by standing right behind it. It is very important that the cog and the pulley are in line. If they are not in line, just take a screwdriver and turn it on the derailleur. If you will turn the screw driver clockwise, you will be able to move the derailleur towards your bike.
Then, you have to turn the derailleur barrel adjuster all the way into its body. After that, you turn it two times back it out. You can found the barrel adjuster at the place where the cable enters its body.
Take the nose pliers and pull the derailleur cable with it. Then, retighten the bolt with the help of the wrench. Now, check whether the chain shifts easily or not. If it is still sluggish, then you have to turn the adjuster towards the bike so that it may get shifted without any kind of delay.
Check the adjustment, by shifting the chain to the smallest and largest rear cog. You will have to check the alignment also before tightening the bolt.