I have been told that it is possible to obtain a Non Immigrant B visa in Bangkok without having to leave Thailand. Is this true? If so, how can it be done?

You cannot get a visa inside the country but most apply for at a Consulate or an Embassy abroad.

What you have been told was probably a way to change your permission to stay from, let's say tourist to employement. That can be done with proper doicumentation through an immigration office.

Thanks, Alex. Yes, I am here on a tourist visa and need to convert to non immigrant visa. I have all the necessary documentation and need to know exactly what the procedure is. Any advice would be greatly appreciated.

The info for that procedure can be found on the immigration website.You do need 23 days on your existing visa (I think).