Fittonias can be challenging to grow as houseplants because they are native to rain forests and so like warmth, high humidity and good moisture for their shallow roots. If they are dry their leaves curl and die, but kept to wet and their stems can rot.
The propagation method we'd recommend is to take tip cuttings (of 2-4 pairs of leaves), dip the base in rooting hormone and insert into a standard potting mixture. Keept it warm and moist and in indirect light.
When the plant is large enough, you can also propage by a type of layering method. For this, put your pot into a large pot and fill the outer pot with peat-based soil with a small amount of sand or perlite sprinkled on top. Bring the growing tips into contact with the soil, and soon you will have rooted babies which can be severed from the mother plant when they are firmly rooted on their own.