This purchase is the most delicate operation. Indeed, the Thai land law regulated by the land code, by the Ministry of Interior, by the civil and commercial code and by the 1975 reform on agricultural land does not allow a foreigner to own a land under his own name. However, the Investment Law does allow it.
In practice, it is therefore impossible to buy land directly, unless you are in one of two situations:

a – You are a foreigner who transfers 40,000,000 baht to Thailand (about 1.1 million euros) in order to invest in different sectors and then you get an authorization to buy land from the Ministry of Interior.  In this case you will be able to own for life a land of 1 Rai (about 1600 m2) or more since since September 2011 the law does not give any limit anymore.
In practice this option is almost never realized. Notably because it concerns few people.

b- You are a foreigner who creates a company of type LLC -in which you must have a minority participation- registered in Thailand. This company in your name can then buy any type of construction and land.
However this company will be seriously controlled by the land department, it will have to have a proven activity and your Thai associates -your co-shareholders- will have to be really involved (no nominee).
The LLC for example requires 3 co-shareholders with only one director (often the foreigner).
In practice this solution can be good only if you sincerely want to create a company and then own land; if your only goal is to own land it is a real ordeal, between finding reliable partners, a competent accountant and lawyer and then proving to the authorities that your company is working well…

In the end, the purchase of land by a foreigner is reserved either to a single person able to bring 1 million euros to Thailand, or to a real entrepreneur whose company will be able to buy any type of property.
Option: you are married with a Thai and in this case you buy the land in his name. You can imagine the consequences in case of separation.