There are a couple ways to go about it. First there is no visa called a marriage visa. There is a Non-Immigrant Type-O <-other which is issued for a variety of reasons, marriage being one..
To get a "yearly extension of stay based on marriage to a thai national, you'd need 400K baht in a thai bank account in your name for 60 days before you apply at the immigration office for the extension, OR you'd need a letter from your embassy stating you had income of 40K baht per month. There is also documentation like the thai marriage certificates, copy of your freedom to marry affidavit, pictures of you & your wife standing in front of the address numbers where you live, a couple pictures of the wedding, and couple of you two sitting around the house.
A lot of people who don't meet or don't want to meet the financial criteria for an in country extension of stay go to the Thai Embassy in Savannakhet Lao and get a year-long, multi-entry Non-Immigrant Type-O visa.. They don't require proof of financials there and that visa is good for 90 days at a time in country, then you exit/re-enter and get another 90 days. You do this for the entire year..