First 3 months you can drive on your UK licence. Then you should (but some do not) go to the Transport Office and they will after a few easy tests, issue you a Thai licence. Note that car and bike are separate licences. You can purchase a car or bike. Very simple and painless but first you need to obtain a residency certificate from Immigration. Taking a vehicle out of Thailand can be difficult, especially the insurance aspects.
That is the normal method. If the Thai person enters Thailand using their foreign passport then they are treated as a foreign person and need a visa and are subject to 90 day reports etc.