This is the K1 Visa in Thailand. As an American in Thailand you have two basic options for taking your Thai girlfriend back to the US. The first is to apply for a US K1 visa for a Thai fiancée, or you can get married in Thailand and apply for a K3 spouse visa for a Thai or a CR1 visa.
K1 Visa in Thailand
The fiancée visa is valid for 90 days and you will need to get married. The visa is valid for 90 days once she enters the US. Should she not get married during the 90 days, she will have to leave the United States for Thailand or risk overstay, arrest and deportation. See also the K3 visa as well as a K2 visa.
The US Fiancée Visa Process
You have to complete your petition and file this with the USCIS in the US. Note you can start the process in Thailand if you have live in Thailand for many years. You now have to wait about two weeks and the USCIS will send you a letter to acknowledge your application. This tells you that the process has now started.
Usually after 2 months they will send you another letter to tell you that the application has been approved. This will now be forward by them to the NVC (National Visa Centre). They will review your application further and process all the documents.
Again after about a month the National Visa Center will forward the packet to the US Embassy in Bangkok for further investigation and processing. The US Embassy in Bangkok will now notify your Thai fiancée what is needed. This is a list of documents that will be needed. They call this package 3.
The document collection process does take a while and she will need to collect all the documents for the process to be completed. These need to be submitted and these documents will include a health certificate as well as a criminal clearance certificate from Bangkok Police. The process takes about 6 months to complete at the fastest.
Note that if your fiancée has a child then you will need to speak to an attorney about another visa for the child. Normally they would start the process for both visa at the same time. You should ask about the K2 visa application process for a minor child as well as the cost for this.
The most common problems in Thailand with the K1 Visa from Thailand is where the applicant has overstayed a visa before and had to be deported. This creates problems as you might not be able to apply for a visa for her again. You would have to wait until such time that another visa can be applied for. Medical checks as well a police records checks are usually not an issue.
Always take legal advice from a lawyer in Thailand who can assist you with the process as an error can create a delay and this can be costly. The appeals process is long, costly and very difficult. Always start or the proper legal footing.