Cats and kittens should be transported in a special cat carrier. A warm towel placed inside the carrier will create a safe place for the kitten, which will have no real concept about the journey or its new home.
It is important to use a cat carrier because a frightened kitten may panic when first placed in a vehicle with someone unfamiliar.
Pick up the kitten gently by supporting its bottom with one hand and place it in the carrier. Clopse the carrier quickly and secure the fastener. Place the carrier on your or your helper's knees to prevent any sudden movements which may cause the carrier and the kitten to be thrown about.
It is important not to leave the kitten unattended while it is inside the carrier. It is also vital to make sure that it cannot become either too hot or too cold.
This trip is usually the first time that the kitten has travelled in a car and that is probably frightening for a kitten. This is also the first time that the kitten is separated from its litter siblings.