If you are planning to visit Thailand for a short duration, you would usually get yourself a prepaid mobile data plan. Upon arrival at the airport, do visit the booth of AIS, True and DTAC where you can select a mobile plan that may best suit your needs. There are plans that cater for 4, 7 or 14 days… some are unlimited data plan.
However if you intend to stay in Thailand for a long duration…. the other option is to obtain a postpaid line whereby you sign up for a specific package which provides a fixed voice call/data allowance each month… either following the calendar month or your bill cycle.
You can inquire about the issuance of postpaid line at any sales office of a telecommunication company of your choice, usually located in many shopping complex like Central Plaza.
Issuance of a postpaid line is subjected to approval from the telecommunication company and if you are a foreigner, a local resident guarantor (usually their customer with good record standing) is required. The guarantor would be held accountable to settle the bills of the foreigner in the event there is outstanding and the foreigner could not be contacted.
Due to the financial liability, locals may be very reluctant to be a guarantor. After all, unlike prepaid, you can call all you want using a postpaid line and then settle when the bill comes later. But if there is a guarantor and the telecommunication company has agreed to issue, there would be a set of forms where both the guarantor and the applicant is required to complete.
Usually postpaid lines would be issued under an organization or company for the foreigner who may come in under employment visa.
When you first get the prepaid line, you usually do not need to pay any charges until the bill comes in more than a month later. Then you would be billed based on your usage- ie if you are entitled to 150 min free voice call to local numbers and you have exceeded that, then you would be billed for the amount that you have exceeded.