Tuk-tuks are plentiful in Patong and Phuket Town but travel to many areas in the north or south part of the island may require you to negotiate a round trip rate because finding a tuk-tuk for the return trip may be difficult. Note that there are no seatbelts in a Tuk-tuk.
The rate paid is by the distance traveled not by the number of passengers. If the driver wants to charge you by the number of people, wave him on and catch another.
The polite way to stop a songthaew or tuk-tuk on the street is to hold your arm out in front of you, palm down and make a up and down motion.