You will need to get your marriage certificate legalised in your home country, then translated. You will need to send both marriage certificate and translated copy to Thai Embassy in your home country for verification of translation. Then you can obtain a non immigrant 'O' visa based on marriage provided you meet all the other criteria. Good luck.
Just ensure you have enough money. I'd allow upwards of 500,000 Thb per year to live, plus 800,000 to be deposited in a Thai bank for your visa. Enter Thailand visa exempt and then apply for a Non immigrant 'O' visa when you're here. Simple as that.
I'm 60 with pre-existing conditions. Quoted $6,000 per year, excluding pre-existing conditions (which are the ones most likely to kill me).
Have set enough aside to hopefully cover at least one major illness/injury. Saving $6k per year, I can set aside 1 million Baht every 4 years for medical care in the future.