If you are currently living in Thailand, please see the links in my article on A Brief Survey of Thai Bible Translations.

Living Outside of Thailand?

If you are living outside of Thailand, you can order directly from the Thailand Bible Society in Bangkok, and they will ship internationally to you.  The postage will be expensive but you'll have lots of choices in Bibles (Thai only, Thai-English, NT only, etc.).  The Thailand Bible Society produces the Thai Standard Version that is used in the majority of Thai church.  To order, click here to go to the Thailand Bible Society website.

Alternatively, you can try ordering from a Bible society (such as International Bible Society/Biblica) or website (such as Amazon.com) located in your home country.

In the USA

Thai Standard Version might be available from the American Bible Society. See their website or contact them to ask.

The Thai Easy-to-Read New Testament is available from the Bible League International as a free download.  They used to have it for sale as a printed book but it doesn't seem to be on the website anymore.  You might contact them to see if they still have any available for purchase.

In the UK 

In the UK, you can get either a full Bible (version unknown) or a Thai/English New Testament (update of Thai standard version) from the website of the Bible Society.

Online 

Multiple versions of the Thai Bible are available online at the YouVersion website.

The Thailand Bible Society has a Thai Bible iPhone app in the iTunes store.

The Thai Easy-to-Read New Testament is available from the Bible League International as a free download.

An NIV-like translation of the Thai Bible is available from the International Bible Society for download at their website.

The Thai King James Version (KJV) is available for purchase or download from Philip Pope's website.  

An audio Thai Bible, a free MP3 download is available at Faith Comes by Hearing