A non-resident can get a work permit for Thailand.  It is not easy, but it can be done.  The work permit is tied to your Visa, and the determining factor is the length of stay you have been allowed by The Kingdom of Thailand.  Always be sure your Visa has been extended to accommodate a work schedule.

A company that hires you must fill out the paperwork involved in obtaining a work permit.  Once that is done, a long process ensues that may require that you leave Thailand for a neighboring country, only to re-enter.  Please check with your Consulate for the latest details concerning obtaining a Thai work permit.

Working from home on the internet for companies outside of Thailand will not cause concern from the Thai government.  

You can also start your own company once you are in Thailand.  Coming into the country on a Tourist Visa is enough for you to begin the paperwork involved in starting a company.  The Visa can always be extended into a Non-Immigrant Business Visa.  

One of the most popular ways of earning a living as a foreigner in Thailand is to teach.  While the pay scale isn’t high, it will provide an income.  Also, you can teach privately, thus earning more per hour.  Weekend private tutoring is the highest paid (around $20US/hour) form of freelancing you can do;  however in the outlying areas, that fee will be less.