Some medical professionals more or less discretely advertise for abortion business, but many abortionists are untrained, which commonly leads to the dreadful consequences.
So, abortion in Thailand is de jure legal only when it is considered necessary to protect a woman's health or in case of rape. Under the recently revised (but yet published) abortion regulations issued by the Medical Council of Thailand, the term "health" includes mental, emotional and physiological considerations as well as physical conditions. The determination that a woman qualifies for a legal abortion under that criteria can only be made by a medical doctor licensed in Thailand.
This determination (and, if positive, the abortion procedure) can be done at any hospital, private or government. Though, private hospitals with religious affiliations may chose not provide that service. In early pregnancy, it can also be done at one of the many low cost clinics operated by the Thai NGO Population & Community Development Association (PDA). For cost estimates, contact the hospital or clinic of your choice. Just remember that they will not tell you if they will be able to perform the procedure until the woman has met with a doctor.