Tourist visas are valid for 3 months but you only get 2 months on arrival. After the 2 months you can goto immigration with a passport photo and 1900 baht and get another 30 days. After that you must cross a border to activate your next entry. When you have done that and your 60 days is up again you can then get a further 30 days at immigration.
Warning.....When you are looking at doing your final border crossing check the dates. You must leave on the date,preferrably the day before, your VISA expires. That is the "enter before date" on the blue Tourist Visa sticker and not the "permitted to stay" stamp that you got at immigration. If you miss it they will only stamp you for 15 days at the border and not 60.