You first have to visit your embassy and get an 'Affirmation of Marital Status' certificate, you then have it translated by an official translator and then take it, or have it sent, to the Ministry of Foreign Affairs to have it legalised.
You can then visit an Amphur and use this form , and any other form that they ask for' to get married.
( And may the Lord have mercy upon your soul , just joking)