There are a number of travel options when in Thailand. Traveling in Thailand is inexpensive though not always fast. There are local buses in the cities but they may be crowded, so it is a good idea to rent a car when you are in Thailand (check for damages before you rent the car or the car owner will charge you for them later). Train is the prefered mode of transport for long distance travel. Please ask a local travel agent to help you with reservations.
Do note that foreigners may have to pay a bit more for long distance train tickets than locals. Women are recommended to travel with companions and it is better to avoid night travel.
If you want to go to another island, take a ferry. All major Thai islands are connected to the mainland by ferries. Avoid traveling on boats that are in poor condition or overcrowded. You might have to wait for some time for the next ferry to depart but its worth it. Ferry prices are very cheap and you must buy the tickets inboard. There are speedboats too but those cost a lot more.
If you don’t mind the cost, consider taking a flight. All the major cities are connected by plane. In some cases, you can save a lot of time and effort by traveling by plane. For example, the journey from Chiang Mai to Phuket can take days by road but it is only two hours by plane. There are a number of low cost carriers to consider...