First see how the Rishyadi Nyasas are done. These Nyasas are done with the right hand using the Tattva Mudra/Nyasa Mudra which is formed by joining the thumb and the ring finger at the tips.
When you say " ... vagdevata rshiayah" touch the top of your head with the right hand in Tattva Mudra.
While saying "Anushtupa Chandah" touch similarly the upper lips (or upper porting of the upper lip).
While specifying the Devata (Sri Lalita Parameswari Devata) touch the heart (middle of the chest).
While saying "Srimad vagbhavakuteti bijam" touch similarly the right shoulder.
While saying " Madhya kuteti shakti" touch the left shoulder with the same Mudra.
And, while saying "Shaktikuteti Kilakam" similarly touch the navel.
Here ends, Rishyadi Nyasas.
Next comes the Kara Nyasas:
While saying "Aim angushtabhyam namaha" run all four fingers from the base till the tip of the thumb. While saying " Kilm tarjanibhayam namaha" run the thumb from the base till the tip of the index finger. Similarly we do for the remaining fingers ( Anamika=ring finger, Madhyama=middle finger and Kanishtika=Little finger).
These Nyasas are done on both the hands simultaneously.
And, while saying "Aim karatala kara prishtabhyam namaha" open both the palms; run the opened palms of the right hand on the front and back sides of the left palm and repeat the same for the other palm) (Reference-Astrojyoti.com)
And, then comes Anga Nyasas:
While saying "Aim hridaya namaha" touch the region of heart with the right hand's index, middle and ring fingers (leaving the thumb and little fingers out).
While saying "Klim shirase swaha" touch the top of the head with the right hand's middle and ring fingers.
While saying "Sauh shikhayai vaushat" touch the back side of the head with the right hand thumb only.
While saying "Sauh kavachaya hum" keep the right hand open palm on the left shoulder and the left hand open palm on the right shoulder with the hands crossing each other or else do like this - cross both the hands and run the fully opened palms from shoulders to finger tips.
While saying "Klim netratraya oushat" open the three fingers - index, middke and ring - of the right hand and place the index on the right eye, middle on the third eye (middle of the eyebrow) and the ring on the left.
While saying "Aim astraya phat" do this - open up the left palm and strike it three times with index and middle fingers of the right hand.
While saying "Bhurbhuvasuvariti digvandaha" we draw a protective circle around us by doing like this - by using right hand thumb and middle fingers make rattle clockwise around the head. (there should be eight rattles made signifying the eight directions).
Note of caution:
If you do not have any experiences with how to do Nyasas then it is unlikely that you can follow the steps given and do it correctly. Also, not everyone can do these Nyasas. Only after initiations the Guru will teach these things to the disciples.